QG - Vertices

P1={1,0,0};P2={0,1,0};P3={0,0,1};P4={p,q,r};

Circular Points at infinity

CI1={-(a^2)+(b^2)-(c^2)-(Sqrt[-4 (b^2) (c^2)+(((-(a^2)+(b^2)+(c^2)))^2)]),(a^2)-(b^2)-(c^2)+(Sqrt[-4 (b^2) (c^2)+(((-(a^2)+(b^2)+(c^2)))^2)]),2 (c^2)};
CI2={-(a^2)+(b^2)-(c^2)+(Sqrt[-4 (b^2) (c^2)+(((-(a^2)+(b^2)+(c^2)))^2)]),(a^2)-(b^2)-(c^2)-(Sqrt[-4 (b^2) (c^2)+(((-(a^2)+(b^2)+(c^2)))^2)]),2 (c^2)};

QG - Points

QGP1={p,0,r};  (* Diagonal Crosspoint *)
QGP2={-p (q+r),-q (p+2 q+r),(-p-q) r};  (* Midpoint of the 3rd QA-Diagonal *)
QGP3={-p (p+q),q (-p+r),r (q+r)};  (* Midpoint of the 3rd QL-Diagonal *)
QGP4={-3 (p^3)-3 (p^2) q-9 (p^2) r-9 p q r-3 (q^2) r-9 p (r^2)-6 q (r^2)-3 (r^3),-3 (p^3)-9 (p^2) q-6 p (q^2)-9 (p^2) r-18 p q r-6 (q^2) r-9 p (r^2)-9 q (r^2)-3 (r^3),-3 (p^3)-6 (p^2) q-3 p (q^2)-9 (p^2) r-9 p q r-9 p (r^2)-3 q (r^2)-3 (r^3)}; (* 1st Quasi Centroid *)
QGP5={-((b^2)-(c^2)) p ((c^2) q+(b^2) r)-(a^4) ((p^2)+r (2 q+r)+p (q+2 r))+(a^2) ((b^2) ((p^2)+(r^2)+p (q+r))+(c^2) ((p^2)+2 p r+r (2 q+r))),(b^2) (-(b^2) ((p^2)+p q+r (q+r))+(a^2) ((p^2)+r (3 q+r)+p (q+2 r))+(c^2) ((p^2)+r (q+r)+p (3 q+2 r))),-(b^4) p r+(a^4) q r+(b^2) (c^2) ((p^2)+p r+r (q+r))-(c^4) ((p^2)+2 p (q+r)+r (q+r))+(a^2) ((b^2) (p-q) r+(c^2) ((p^2)+(r^2)+2 p (q+r)))};  (* 1st Quasi Circumcenter *)
QGP6={-(a^4) ((p^2)+2 p (q+r)+r (3 q+r))+2 (a^2) ((c^2) q r+(b^2) (p q-p r-q r))+((b^2)-(c^2)) ((b^2) ((p^2)+r (q+r))-(c^2) ((p^2)+2 p (q+r)+r (q+r))),((b^2) (-p+r)+(a^2) (p+r)-(c^2) (p+r)) ((b^2) (p-r)+(a^2) (p+2 q+r)-(c^2) (p+2 q+r)),(b^4) ((p^2)+p q+(r^2))-(c^4) ((p^2)+3 p q+2 p r+2 q r+(r^2))-2 (b^2) (c^2) (-q r+p (q+r))+(a^4) ((p^2)+r (2 q+r)+p (q+2 r))-2 (a^2) (-(c^2) p q+(b^2) ((p^2)+p (q+r)+r (q+r)))};  (* 1st Quasi Orthocenter *)
QGP7={-(a^4) q (p+r)-(a^2) ((c^2) (((p+r))^2)+(b^2) ((p^2)-p q+3 p r+2 q r+(r^2)))+((b^2)-(c^2)) (-(c^2) (p+r) (p+q+r)+(b^2) ((p^2)+p r+r (q+r))),(a^4) (p+r) (p+2 q+r)+(c^4) (p+r) (p+2 q+r)+(b^4) (q r+p (q+2 r))-(b^2) (c^2) ((p^2)+r (3 q+r)+p (q+2 r))-(a^2) (2 (c^2) (p+r) (p+2 q+r)+(b^2) ((p^2)+r (q+r)+p (3 q+2 r))),-(c^4) q (p+r)+(a^4) (p+r) (p+q+r)-(b^2) (c^2) ((p^2)+2 p q+3 p r-q r+(r^2))+(b^4) ((p^2)+(r^2)+p (q+r))-(a^2) ((c^2) (((p+r))^2)+(b^2) (2 (p^2)+r (q+2 r)+p (2 q+3 r)))};  (* 1st Quasi Nine-point Center *)
QGP8={-12 (p^6)-9 (p^5) q-63 (p^5) r-39 (p^4) q r-135 (p^4) (r^2)-66 (p^3) q (r^2)-150 (p^3) (r^3)-54 (p^2) q (r^3)-90 (p^2) (r^4)-21 p q (r^4)-27 p (r^5)-3 q (r^5)-3 (r^6),-3 (p^6)-6 (p^5) q-18 (p^5) r-30 (p^4) q r-45 (p^4) (r^2)-60 (p^3) q (r^2)-60 (p^3) (r^3)-60 (p^2) q (r^3)-45 (p^2) (r^4)-30 p q (r^4)-18 p (r^5)-6 q (r^5)-3 (r^6),-3 (p^6)-3 (p^5) q-27 (p^5) r-21 (p^4) q r-90 (p^4) (r^2)-54 (p^3) q (r^2)-150 (p^3) (r^3)-66 (p^2) q (r^3)-135 (p^2) (r^4)-39 p q (r^4)-63 p (r^5)-9 q (r^5)-12 (r^6)};  (* 2nd Quasi Centroid *)
QGP9={-(a^4) (p+r) (2 p+2 q+r)-((b^2)-(c^2)) p (-(c^2) (p+r)+(b^2) (p+q+2 r))+(a^2) ((c^2) (p+r) (3 p+2 q+r)+(b^2) (3 (p^2)+(r^2)+3 p (q+r))),(b^2) (-(b^2) ((p^2)+p q+r (q+r))+(a^2) ((p^2)+r (3 q+r)+p (q+2 r))+(c^2) ((p^2)+r (q+r)+p (3 q+2 r))),-(a^4) r (p+r)-(b^4) r (2 p+q+r)-(c^4) (p+r) (p+2 (q+r))+(b^2) (c^2) ((p^2)+3 p r+3 r (q+r))+(a^2) ((b^2) r (3 p+q+2 r)+(c^2) (p+r) (p+2 q+3 r))};  (* 2nd Quasi Circumcenter *)
QGP10={(a^4) (p (q+r)+r (3 q+r))+2 (a^2) ((b^2) ((p^2)+2 p r+q r)+(c^2) ((p^2)-q r+p (q+r)))-((b^2)-(c^2)) ((b^2) (2 (p^2)+p (q+r)+r (q+r))-(c^2) (2 (p^2)+3 p (q+r)+r (q+r))),(-(b^2) (-p+r)-(a^2) (p+r)+(c^2) (p+r)) ((b^2) (p-r)+(a^2) (p+2 q+r)-(c^2) (p+2 q+r)),(c^4) ((p^2)+q r+p (3 q+r))+2 (b^2) (c^2) ((r^2)+p (q+2 r))-(b^4) ((p^2)+p (q+r)+r (q+2 r))-(a^4) ((p^2)+r (3 q+2 r)+p (q+3 r))+2 (a^2) ((c^2) (p (-q+r)+r (q+r))+(b^2) ((p^2)+2 r (q+r)+p (q+2 r)))};  (* 2nd Quasi Orthocenter *)
QGP11={(a^4) (2 (p^2)-q r+p (q+2 r))-(a^2) ((c^2) (5 (p^2)+4 p q+6 p r+(r^2))+(b^2) (5 (p^2)+3 p q+7 p r+2 q r+(r^2)))+((b^2)-(c^2)) (-(c^2) (3 p+r) (p+q+r)+(b^2) (3 (p^2)+r (q+r)+p (2 q+3 r))),(a^4) (p+r) (p+2 q+r)+(c^4) (p+r) (p+2 q+r)+(b^4) (q r+p (q+2 r))-(b^2) (c^2) ((p^2)+r (3 q+r)+p (q+2 r))-(a^2) (2 (c^2) (p+r) (p+2 q+r)+(b^2) ((p^2)+r (q+r)+p (3 q+2 r))),(a^4) (p+q+r) (p+3 r)+(c^4) (-p q+2 p r+q r+2 (r^2))+(b^4) ((p^2)+p q+3 p r+2 q r+3 (r^2))-(b^2) (c^2) ((p^2)+2 p q+7 p r+3 q r+5 (r^2))-(a^2) ((c^2) ((p^2)+6 p r+4 q r+5 (r^2))+(b^2) (2 (p^2)+2 p q+7 p r+5 q r+6 (r^2)))};  (* 2nd Quasi Nine-point Center *)
QGP12={p (-q+r),-q (p+2 q+r),(p-q) r};  (* Inscribed Harmonic Conic Center *)
QGP13={-p (p+2 q-r),-2 q (p+2 q+r),(p-2 q-r) r};  (* Circumscribed Harmonic Conic Center *)
QGP14={p (q+r) (p q-p r-3 q r-(r^2)),-q (((p-r))^2) (p+2 q+r),(-p-q) r ((p^2)+3 p q+p r-q r)};  (* Center of the M3D Hyperbola *)
QGP15={p (q-r)-r (q+r),-(p+r) (p+2 q+r),-(p^2)+q r-p (q+r)};  (* Kirikami Center *)
QGP16={(a^2) (p+q+r) (-(c^2) (p^2) q-(c^2) p (q^2)+(b^2) (p^2) r+(a^2) p q r+(b^2) p q r-2 (c^2) p q r+(a^2) (q^2) r),-((c^2) p q+(b^2) p r+(a^2) q r) ((a^2) p q-(b^2) p q+(a^2) (q^2)-(b^2) (q^2)+(c^2) (q^2)-(b^2) p r-(b^2) q r+(c^2) q r),(c^2) (p+q+r) ((c^2) p (q^2)-2 (a^2) p q r+(b^2) p q r+(c^2) p q r-(a^2) (q^2) r+(b^2) p (r^2)-(a^2) q (r^2))};  (* Schmidt Point *)
QGP17={-p ((c^2) (p^2) q (q+r)+r ((b^2) (p^2) (q+r)-(a^2) q ((p^2)+q r))),p q r ((a^2) q (p-r)+(c^2) q (-p+r)-(b^2) (p q+2 p r+q r)),(-p-q) ((b^2) p+(a^2) q) (r^3)+(c^2) p q r (p q+(r^2))};  (* Perpendicular projection QG-P1 on QG-L1 = CSC(QGP18) *)QGP18={-(a^2) q r ((p+q) ((b^2) p+(a^2) q) (r^2)-(c^2) p q (p q+(r^2))),-p r ((b^4) p (p+q) r (q+r)-((a^2)-(c^2)) (q^2) ((a^2) (p+q) r-(c^2) p (q+r))+(b^2) q (-(a^2) (p+q) (p-q-r) r+(c^2) p (p+q-r) (q+r))),-(c^2) p q ((c^2) (p^2) q (q+r)+r ((b^2) (p^2) (q+r)-(a^2) q ((p^2)+q r)))};  (* 1st Quasi Isogonal Conjugate QG-L1 *)QGP19={(a^2) q r ((p+q) ((b^2) p+(a^2) q) (r^2)+(c^2) p q (p q-(r^2))),-p r ((b^4) p (p+q) r (q+r)-((a^2)-(c^2)) (q^2) ((a^2) (p+q) r-(c^2) p (q+r))+(b^2) q (-(a^2) (p+q) (p-q-r) r+(c^2) p (p+q-r) (q+r))),(c^2) p q ((c^2) (p^2) q (q+r)+r ((b^2) (p^2) (q+r)+(a^2) q (-(p^2)+q r)))};  (* 2nd Quasi Isogonal Crosspoint *)

QG2P1a={(a^4) (p^2) (q^2)-2 (a^2) (b^2) (p^2) (q^2)+(b^4) (p^2) (q^2)-2 (b^2) (c^2) (p^2) (q^2)+(c^4) (p^2) (q^2)+2 (a^4) (p^2) q r-2 (a^2) (b^2) (p^2) q r-2 (a^2) (c^2) (p^2) q r+2 (a^4) p (q^2) r-2 (a^2) (b^2) p (q^2) r+2 (a^2) (c^2) p (q^2) r+(a^4) (p^2) (r^2)+(b^4) (p^2) (r^2)-2 (a^2) (c^2) (p^2) (r^2)-2 (b^2) (c^2) (p^2) (r^2)+(c^4) (p^2) (r^2)+2 (a^4) p q (r^2)+2 (a^2) (b^2) p q (r^2)-2 (a^2) (c^2) p q (r^2)+2 (a^4) (q^2) (r^2),-(a^2) (c^2) (p^2) (q^2)-(b^2) (c^2) (p^2) (q^2)+(c^4) (p^2) (q^2)+(a^4) p (q^3)-2 (a^2) (b^2) p (q^3)+(b^4) p (q^3)-2 (a^2) (c^2) p (q^3)-2 (b^2) (c^2) p (q^3)+(c^4) p (q^3)+(a^4) p (q^2) r-2 (a^2) (b^2) p (q^2) r+(b^4) p (q^2) r-2 (a^2) (c^2) p (q^2) r-2 (b^2) (c^2) p (q^2) r+(c^4) p (q^2) r+(a^2) (b^2) (p^2) (r^2)+(b^4) (p^2) (r^2)-(b^2) (c^2) (p^2) (r^2)+(a^4) p q (r^2)+2 (a^2) (b^2) p q (r^2)+(b^4) p q (r^2)-2 (a^2) (c^2) p q (r^2)-2 (b^2) (c^2) p q (r^2)+(c^4) p q (r^2)+(a^4) (q^2) (r^2)+(a^2) (b^2) (q^2) (r^2)-(a^2) (c^2) (q^2) (r^2)+(Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((a^2) (p^2) (q^2)-(b^2) (p^2) (q^2)+(a^2) p (q^3)-(b^2) p (q^3)+(c^2) p (q^3)+(a^2) (p^2) q r-(b^2) (p^2) q r-(c^2) (p^2) q r+2 (a^2) p (q^2) r+2 (a^2) (q^3) r-(b^2) (p^2) (r^2)+(a^2) (q^2) (r^2)),-(Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((c^2) (p^2) (q^2)-(a^2) (p^2) q r+(b^2) (p^2) q r+(c^2) (p^2) q r-(a^2) (p^2) (r^2)+(c^2) (p^2) (r^2)-(a^2) p q (r^2)-(b^2) p q (r^2)+(c^2) p q (r^2)-(a^2) (q^2) (r^2))+((a^2)-(b^2)+(c^2)) ((c^2) (p^2) (q^2)+(a^2) p (q^2) r-(b^2) p (q^2) r+(c^2) p (q^2) r-(b^2) (p^2) (r^2)+(a^2) (q^2) (r^2))}; (* 1st Inscribed Square Center *)
QG2P1b={(a^4) (p^2) (q^2)-2 (a^2) (b^2) (p^2) (q^2)+(b^4) (p^2) (q^2)-2 (b^2) (c^2) (p^2) (q^2)+(c^4) (p^2) (q^2)+2 (a^4) (p^2) q r-2 (a^2) (b^2) (p^2) q r-2 (a^2) (c^2) (p^2) q r+2 (a^4) p (q^2) r-2 (a^2) (b^2) p (q^2) r+2 (a^2) (c^2) p (q^2) r+(a^4) (p^2) (r^2)+(b^4) (p^2) (r^2)-2 (a^2) (c^2) (p^2) (r^2)-2 (b^2) (c^2) (p^2) (r^2)+(c^4) (p^2) (r^2)+2 (a^4) p q (r^2)+2 (a^2) (b^2) p q (r^2)-2 (a^2) (c^2) p q (r^2)+2 (a^4) (q^2) (r^2),-(a^2) (c^2) (p^2) (q^2)-(b^2) (c^2) (p^2) (q^2)+(c^4) (p^2) (q^2)+(a^4) p (q^3)-2 (a^2) (b^2) p (q^3)+(b^4) p (q^3)-2 (a^2) (c^2) p (q^3)-2 (b^2) (c^2) p (q^3)+(c^4) p (q^3)+(a^4) p (q^2) r-2 (a^2) (b^2) p (q^2) r+(b^4) p (q^2) r-2 (a^2) (c^2) p (q^2) r-2 (b^2) (c^2) p (q^2) r+(c^4) p (q^2) r+(a^2) (b^2) (p^2) (r^2)+(b^4) (p^2) (r^2)-(b^2) (c^2) (p^2) (r^2)+(a^4) p q (r^2)+2 (a^2) (b^2) p q (r^2)+(b^4) p q (r^2)-2 (a^2) (c^2) p q (r^2)-2 (b^2) (c^2) p q (r^2)+(c^4) p q (r^2)+(a^4) (q^2) (r^2)+(a^2) (b^2) (q^2) (r^2)-(a^2) (c^2) (q^2) (r^2)-(Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((a^2) (p^2) (q^2)-(b^2) (p^2) (q^2)+(a^2) p (q^3)-(b^2) p (q^3)+(c^2) p (q^3)+(a^2) (p^2) q r-(b^2) (p^2) q r-(c^2) (p^2) q r+2 (a^2) p (q^2) r+2 (a^2) (q^3) r-(b^2) (p^2) (r^2)+(a^2) (q^2) (r^2)),(Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((c^2) (p^2) (q^2)-(a^2) (p^2) q r+(b^2) (p^2) q r+(c^2) (p^2) q r-(a^2) (p^2) (r^2)+(c^2) (p^2) (r^2)-(a^2) p q (r^2)-(b^2) p q (r^2)+(c^2) p q (r^2)-(a^2) (q^2) (r^2))+((a^2)-(b^2)+(c^2)) ((c^2) (p^2) (q^2)+(a^2) p (q^2) r-(b^2) p (q^2) r+(c^2) p (q^2) r-(b^2) (p^2) (r^2)+(a^2) (q^2) (r^2))}; (* 2nd Inscribed Square Center *)
QG2P2a={p,q,0};  (* 1st Endpoint QA-Diagonal *)
QG2P2b={0,q,r}; (* 2nd Endpoint QA-Diagonal *)
QG2P3a={p,0,-r};  (* 1st Endpoint QA-Diagonal *)
QG2P3b={p,2 q,r}; (* 2nd Endpoint QA-Diagonal *)
QG2P4a= {-2 ((a^2)-(b^2)+(c^2)) (-(c^2) (p^2) (q^2)+(a^2) (p^2) q r-(b^2) (p^2) q r-(c^2) (p^2) q r+(a^2) p (q^2) r-(b^2) p (q^2) r+(c^2) p (q^2) r-(b^2) (p^2) (r^2)-(a^2) p q (r^2)-(b^2) p q (r^2)+(c^2) p q (r^2)-(a^2) (q^2) (r^2))+(Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (2 (c^2) (p^3) q+2 (c^2) (p^2) (q^2)-(a^2) (p^3) r+(b^2) (p^3) r+(c^2) (p^3) r-2 (a^2) (p^2) q r+2 (b^2) (p^2) q r-2 (b^2) p q (r^2)+2 (c^2) p q (r^2)-2 (a^2) (q^2) (r^2)-(a^2) p (r^3)-(b^2) p (r^3)+(c^2) p (r^3)-2 (a^2) q (r^3)),-2 (a^2) (c^2) (p^2) (q^2)+2 (b^2) (c^2) (p^2) (q^2)+2 (c^4) (p^2) (q^2)+(a^4) (p^2) q r-2 (a^2) (b^2) (p^2) q r+(b^4) (p^2) q r-2 (a^2) (c^2) (p^2) q r+6 (b^2) (c^2) (p^2) q r+(c^4) (p^2) q r+4 (a^2) (c^2) p (q^2) r+4 (b^2) (c^2) p (q^2) r-4 (c^4) p (q^2) r-2 (a^4) (q^3) r+4 (a^2) (b^2) (q^3) r-2 (b^4) (q^3) r+4 (a^2) (c^2) (q^3) r+4 (b^2) (c^2) (q^3) r-2 (c^4) (q^3) r-2 (a^2) (b^2) (p^2) (r^2)+2 (b^4) (p^2) (r^2)+2 (b^2) (c^2) (p^2) (r^2)-2 (a^4) p q (r^2)+2 (b^4) p q (r^2)+4 (a^2) (c^2) p q (r^2)-2 (c^4) p q (r^2)-4 (a^4) (q^2) (r^2)+6 (a^2) (b^2) (q^2) (r^2)-2 (b^4) (q^2) (r^2)+6 (a^2) (c^2) (q^2) (r^2)+4 (b^2) (c^2) (q^2) (r^2)-2 (c^4) (q^2) (r^2)-(a^4) q (r^3)+2 (a^2) (b^2) q (r^3)-(b^4) q (r^3)+2 (a^2) (c^2) q (r^3)+2 (b^2) (c^2) q (r^3)-(c^4) q (r^3)-(Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (-2 (c^2) (p^2) (q^2)-4 (c^2) p (q^3)+(a^2) (p^2) q r-(b^2) (p^2) q r-(c^2) (p^2) q r+4 (a^2) p (q^2) r-4 (b^2) p (q^2) r-4 (c^2) p (q^2) r+2 (a^2) (q^3) r-2 (b^2) (q^3) r+2 (c^2) (q^3) r+2 (a^2) p q (r^2)-4 (b^2) p q (r^2)-2 (c^2) p q (r^2)-2 (b^2) (q^2) (r^2)+2 (c^2) (q^2) (r^2)-2 (b^2) p (r^3)-(a^2) q (r^3)-(b^2) q (r^3)+(c^2) q (r^3)),-4 (c^4) (p^2) (q^2)+4 (a^2) (c^2) (p^2) q r-4 (b^2) (c^2) (p^2) q r-4 (c^4) (p^2) q r+4 (a^2) (c^2) p (q^2) r-4 (b^2) (c^2) p (q^2) r+4 (c^4) p (q^2) r-(a^4) (p^2) (r^2)+2 (a^2) (b^2) (p^2) (r^2)-(b^4) (p^2) (r^2)+2 (a^2) (c^2) (p^2) (r^2)-2 (b^2) (c^2) (p^2) (r^2)-(c^4) (p^2) (r^2)-2 (a^4) p q (r^2)+4 (a^2) (b^2) p q (r^2)-2 (b^4) p q (r^2)+2 (c^4) p q (r^2)-2 (a^4) (q^2) (r^2)+4 (a^2) (b^2) (q^2) (r^2)-2 (b^4) (q^2) (r^2)+4 (b^2) (c^2) (q^2) (r^2)-2 (c^4) (q^2) (r^2)-2 (a^4) q (r^3)+4 (a^2) (b^2) q (r^3)-2 (b^4) q (r^3)+4 (a^2) (c^2) q (r^3)+4 (b^2) (c^2) q (r^3)-2 (c^4) q (r^3)-(a^4) (r^4)+2 (a^2) (b^2) (r^4)-(b^4) (r^4)+2 (a^2) (c^2) (r^4)+2 (b^2) (c^2) (r^4)-(c^4) (r^4)}; (* 1st Intersectionpoint QA-DT-ThalesCircle & QL-DT-ThalesCircle *)
QG2P4b={-2 ((a^2)-(b^2)+(c^2)) (-(c^2) (p^2) (q^2)+(a^2) (p^2) q r-(b^2) (p^2) q r-(c^2) (p^2) q r+(a^2) p (q^2) r-(b^2) p (q^2) r+(c^2) p (q^2) r-(b^2) (p^2) (r^2)-(a^2) p q (r^2)-(b^2) p q (r^2)+(c^2) p q (r^2)-(a^2) (q^2) (r^2))-(Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (2 (c^2) (p^3) q+2 (c^2) (p^2) (q^2)-(a^2) (p^3) r+(b^2) (p^3) r+(c^2) (p^3) r-2 (a^2) (p^2) q r+2 (b^2) (p^2) q r-2 (b^2) p q (r^2)+2 (c^2) p q (r^2)-2 (a^2) (q^2) (r^2)-(a^2) p (r^3)-(b^2) p (r^3)+(c^2) p (r^3)-2 (a^2) q (r^3)),-2 (a^2) (c^2) (p^2) (q^2)+2 (b^2) (c^2) (p^2) (q^2)+2 (c^4) (p^2) (q^2)+(a^4) (p^2) q r-2 (a^2) (b^2) (p^2) q r+(b^4) (p^2) q r-2 (a^2) (c^2) (p^2) q r+6 (b^2) (c^2) (p^2) q r+(c^4) (p^2) q r+4 (a^2) (c^2) p (q^2) r+4 (b^2) (c^2) p (q^2) r-4 (c^4) p (q^2) r-2 (a^4) (q^3) r+4 (a^2) (b^2) (q^3) r-2 (b^4) (q^3) r+4 (a^2) (c^2) (q^3) r+4 (b^2) (c^2) (q^3) r-2 (c^4) (q^3) r-2 (a^2) (b^2) (p^2) (r^2)+2 (b^4) (p^2) (r^2)+2 (b^2) (c^2) (p^2) (r^2)-2 (a^4) p q (r^2)+2 (b^4) p q (r^2)+4 (a^2) (c^2) p q (r^2)-2 (c^4) p q (r^2)-4 (a^4) (q^2) (r^2)+6 (a^2) (b^2) (q^2) (r^2)-2 (b^4) (q^2) (r^2)+6 (a^2) (c^2) (q^2) (r^2)+4 (b^2) (c^2) (q^2) (r^2)-2 (c^4) (q^2) (r^2)-(a^4) q (r^3)+2 (a^2) (b^2) q (r^3)-(b^4) q (r^3)+2 (a^2) (c^2) q (r^3)+2 (b^2) (c^2) q (r^3)-(c^4) q (r^3)+(Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (-2 (c^2) (p^2) (q^2)-4 (c^2) p (q^3)+(a^2) (p^2) q r-(b^2) (p^2) q r-(c^2) (p^2) q r+4 (a^2) p (q^2) r-4 (b^2) p (q^2) r-4 (c^2) p (q^2) r+2 (a^2) (q^3) r-2 (b^2) (q^3) r+2 (c^2) (q^3) r+2 (a^2) p q (r^2)-4 (b^2) p q (r^2)-2 (c^2) p q (r^2)-2 (b^2) (q^2) (r^2)+2 (c^2) (q^2) (r^2)-2 (b^2) p (r^3)-(a^2) q (r^3)-(b^2) q (r^3)+(c^2) q (r^3)),-4 (c^4) (p^2) (q^2)+4 (a^2) (c^2) (p^2) q r-4 (b^2) (c^2) (p^2) q r-4 (c^4) (p^2) q r+4 (a^2) (c^2) p (q^2) r-4 (b^2) (c^2) p (q^2) r+4 (c^4) p (q^2) r-(a^4) (p^2) (r^2)+2 (a^2) (b^2) (p^2) (r^2)-(b^4) (p^2) (r^2)+2 (a^2) (c^2) (p^2) (r^2)-2 (b^2) (c^2) (p^2) (r^2)-(c^4) (p^2) (r^2)-2 (a^4) p q (r^2)+4 (a^2) (b^2) p q (r^2)-2 (b^4) p q (r^2)+2 (c^4) p q (r^2)-2 (a^4) (q^2) (r^2)+4 (a^2) (b^2) (q^2) (r^2)-2 (b^4) (q^2) (r^2)+4 (b^2) (c^2) (q^2) (r^2)-2 (c^4) (q^2) (r^2)-2 (a^4) q (r^3)+4 (a^2) (b^2) q (r^3)-2 (b^4) q (r^3)+4 (a^2) (c^2) q (r^3)+4 (b^2) (c^2) q (r^3)-2 (c^4) q (r^3)-(a^4) (r^4)+2 (a^2) (b^2) (r^4)-(b^4) (r^4)+2 (a^2) (c^2) (r^4)+2 (b^2) (c^2) (r^4)-(c^4) (r^4)}; (* 2nd Intersectionpoint QA-DT-ThalesCircle & QL-DT-ThalesCircle *)
QG2P5a={(-(a^2)+(c^2)) q-(b^2) (p+q),0,(a^2) q-(c^2) q-(b^2) (q+r)};  (* intersection point QG-Ci2 ^ 1st QG-diagonal *)
QG2P5b={-(c^2) (p^3)+(a^2) p (r^2),p r ((b^2) (p-r)-(a^2) (p+r)+(c^2) (p+r)),-(c^2) (p^2) r+(a^2) (r^3)};  (* intersection point QG-Ci2 ^ 2nd QG-diagonal *)

QG - Circles, Conics and Cubics

QGCi1=-q (2 (c^2) q-(a^2) r+(b^2) r+(c^2) r) (x^2)+(2 (c^2) p q-(a^2) p r+(b^2) p r+(c^2) p r+(a^2) q r-(b^2) q r+(c^2) q r) x y-((a^2)-(b^2)+(c^2)) p r (y^2)+(-(a^2) p q+(b^2) p q+(c^2) p q-2 (a^2) (q^2)+2 (b^2) (q^2)-2 (c^2) (q^2)+2 (b^2) p r+(a^2) q r+(b^2) q r-(c^2) q r) x z+((a^2) p q-(b^2) p q+(c^2) p q+(a^2) p r+(b^2) p r-(c^2) p r+2 (a^2) q r) y z-q ((a^2) p+(b^2) p-(c^2) p+2 (a^2) q) (z^2);  (* QA-DT Thales Circle*)
QGCi2=r (-(a^2) q+(b^2) q+(c^2) q+(b^2) r) (x^2)+(2 (c^2) p q-(a^2) q r+(b^2) q r-(c^2) q r+(a^2) (r^2)+(b^2) (r^2)-(c^2) (r^2)) x y-(c p-a r) (c p+a r) (y^2)+q (-(a^2) p+(b^2) p+(c^2) p-(a^2) r-(b^2) r+(c^2) r) x z+((a^2) (p^2)-(b^2) (p^2)-(c^2) (p^2)+(a^2) p q-(b^2) p q+(c^2) p q-2 (a^2) q r) y z-p ((b^2) p+(a^2) q+(b^2) q-(c^2) q) (z^2);  (* QL-DT Thales Circle*)
QGCo1=(q^2) (r^2) (x^2)+2 p q (r^2) x y+(p^2) (r^2) (y^2)-6 p (q^2) r x z+2 (p^2) q r y z+(p^2) (q^2) (z^2);  (* Inscribed Harmonic Conic *)
QGCo2=r x y-2 q x z+p y z;  (* Circumscribed Harmonic Conic *)
QGCo3=-(((p+q))^2) r x y+q (p-r) (p+2 q+r) x z+p (((q+r))^2) y z;  (* M3D Hyperbola *)
QGCu1=((a^4) q ((p^2) q+(q^3)+2 (q^2) r+2 q (r^2)+(r^3)+p (2 (q^2)+2 q r+(r^2)))+(c^4) q ((p^2) q+(q^3)+2 (q^2) r+2 q (r^2)+(r^3)+p (2 (q^2)+2 q r+(r^2)))+(b^4) (q+r) ((q^3)+3 (q^2) r+4 q (r^2)+(r^3)+(p^2) (q+r)+p (2 (q^2)+4 q r+3 (r^2)))+(b^2) (c^2) ((p^2) (2 (q^2)+2 q r-(r^2))+2 (q^2) ((q^2)+3 q r+2 (r^2))+p (4 (q^3)+8 (q^2) r+2 q (r^2)-(r^3)))-(a^2) (2 (c^2) q ((p^2) q+(q^3)+2 (q^2) r+2 q (r^2)+(r^3)+p (2 (q^2)+2 q r+(r^2)))+(b^2) (2 (q^4)+6 (q^3) r+8 (q^2) (r^2)+4 q (r^3)+(r^4)+2 (p^2) q (q+r)+p (4 (q^3)+8 (q^2) r+6 q (r^2)+(r^3))))) (x^3)+(-(c^4) ((p^2) (3 (q^2)-(r^2))+p (4 (q^3)+6 (q^2) r+2 q (r^2)-(r^3))+q ((q^3)+4 (q^2) r+4 q (r^2)+2 (r^3)))-(b^4) ((q^4)+4 (q^3) r+7 (q^2) (r^2)+6 q (r^3)+(r^4)+2 (p^3) (q+r)+(p^2) (5 (q^2)+10 q r+6 (r^2))+2 p (2 (q^3)+6 (q^2) r+7 q (r^2)+3 (r^3)))-(a^4) (2 (p^3) q+(q^4)+4 (q^3) r+6 (q^2) (r^2)+4 q (r^3)+2 (r^4)+(p^2) (5 (q^2)+6 q r+(r^2))+p (4 (q^3)+10 (q^2) r+8 q (r^2)+3 (r^3)))-(b^2) (c^2) (2 (p^3) (q+r)+(p^2) (8 (q^2)+14 q r+3 (r^2))+p (8 (q^3)+22 (q^2) r+18 q (r^2)+5 (r^3))+2 ((q^4)+4 (q^3) r+6 (q^2) (r^2)+3 q (r^3)+(r^4)))+(a^2) (2 (c^2) ((p^3) q+(q^4)+4 (q^3) r+5 (q^2) (r^2)+3 q (r^3)+(r^4)+p (q+r) (((2 q+r))^2)+(p^2) q (4 q+3 r))+(b^2) (2 (q^4)+8 (q^3) r+14 (q^2) (r^2)+12 q (r^3)+3 (r^4)+2 (p^3) (2 q+r)+2 (p^2) (5 (q^2)+8 q r+4 (r^2))+p (8 (q^3)+22 (q^2) r+24 q (r^2)+11 (r^3))))) (x^2) y+((b^4) (p-r) (((p+q+r))^2) (p+q+2 r)+(c^4) (q r (((q+r))^2)+(p^3) (q+2 r)+(p^2) (3 (q^2)+5 q r+(r^2))+p q ((q^2)+6 q r+5 (r^2)))+(a^4) ((p^4)+(p^3) (3 q+4 r)+(p^2) (3 (q^2)+9 q r+5 (r^2))+r ((q^3)+2 (q^2) r+q (r^2)-(r^3))+p ((q^3)+6 (q^2) r+7 q (r^2)+2 (r^3)))+(b^2) (c^2) (-(p^4)+2 (r^2) (((q+r))^2)+(p^3) (2 q+r)+(p^2) (5 (q^2)+8 q r+5 (r^2))+p (2 (q^3)+5 (q^2) r+10 q (r^2)+7 (r^3)))-(a^2) ((b^2) (2 (p^4)+(p^3) (6 q+7 r)-(r^2) ((q^2)+2 q r+3 (r^2))+(p^2) (6 (q^2)+14 q r+7 (r^2))+p (2 (q^3)+7 (q^2) r+6 q (r^2)+(r^3)))+2 (c^2) ((p^3) (2 q+r)+(p^2) (3 (q^2)+7 q r+2 (r^2))+r ((q^3)+2 (q^2) r+q (r^2)+(r^3))+p ((q^3)+6 (q^2) r+6 q (r^2)+3 (r^3))))) x (y^2)+(-(b^2) (p-r) (((p+q+r))^2) ((c^2) p-(a^2) r)-(a^4) r ((p^3)-(r^3)+2 (p^2) (q+r)+p (((q+r))^2))-(c^4) p (-(p^3)+(p^2) r+2 p r (q+r)+r (((q+r))^2))+2 (a^2) (c^2) p r ((p^2)+(((q+r))^2)+p (2 q+r))) (y^3)+((a^4) (2 (p^3) q+3 (q^4)+6 (q^3) r+6 (q^2) (r^2)+3 q (r^3)+(r^4)+(p^2) (5 (q^2)+4 q r+(r^2))+p (6 (q^3)+8 (q^2) r+5 q (r^2)+2 (r^3)))+(c^4) (2 (p^3) q+3 (q^4)+6 (q^3) r+6 (q^2) (r^2)+3 q (r^3)+(r^4)+(p^2) (5 (q^2)+4 q r+(r^2))+p (6 (q^3)+8 (q^2) r+5 q (r^2)+2 (r^3)))-(b^4) ((p^2) (3 (q^2)+6 q r+2 (r^2))+q ((q^3)+2 (q^2) r+q (r^2)+(r^3))+p (4 (q^3)+10 (q^2) r+7 q (r^2)+3 (r^3)))+(b^2) (c^2) (2 (p^3) (q+2 r)+(p^2) (2 (q^2)+14 q r+9 (r^2))+2 q ((q^3)+4 (q^2) r+4 q (r^2)+2 (r^3))+p (2 (q^3)+16 (q^2) r+16 q (r^2)+5 (r^3)))-(a^2) (2 (c^2) (2 (p^3) q+3 (q^4)+6 (q^3) r+6 (q^2) (r^2)+3 q (r^3)+(r^4)+(p^2) (5 (q^2)+4 q r+(r^2))+p (6 (q^3)+8 (q^2) r+5 q (r^2)+2 (r^3)))+(b^2) (2 (q^4)+8 (q^3) r+12 (q^2) (r^2)+8 q (r^3)+(r^4)+2 (p^3) (q+r)+2 (p^2) ((q^2)+3 q r+3 (r^2))+p (2 (q^3)+8 (q^2) r+12 q (r^2)+5 (r^3))))) (x^2) z-2 ((b^2) (c^2) (3 (p^3) r+2 p q r (q+2 r)+(r^2) ((q^2)-(r^2))+(p^2) (-(q^2)+4 q r+4 (r^2)))+(a^4) ((p^4)+3 (p^3) (q+r)+(p^2) (5 (q^2)+7 q r+3 (r^2))+p (4 (q^3)+9 (q^2) r+7 q (r^2)+(r^3))+q ((q^3)+4 (q^2) r+5 q (r^2)+3 (r^3)))+(c^4) ((q^4)+4 (q^3) r+5 (q^2) (r^2)+3 q (r^3)+(r^4)+(p^3) (3 q+r)+(p^2) (5 (q^2)+7 q r+3 (r^2))+p (4 (q^3)+9 (q^2) r+7 q (r^2)+3 (r^3)))-(b^4) ((p^3) (3 q+4 r)+(p^2) (6 (q^2)+13 q r+7 (r^2))+q ((q^3)+4 (q^2) r+6 q (r^2)+3 (r^3))+p (4 (q^3)+12 (q^2) r+13 q (r^2)+4 (r^3)))-(a^2) ((b^2) ((p^4)+(q^2) (r^2)-(p^2) (((q+2 r))^2)-p r (2 (q^2)+4 q r+3 (r^2)))+(c^2) ((p^4)+2 (q^4)+8 (q^3) r+10 (q^2) (r^2)+6 q (r^3)+(r^4)+(p^3) (6 q+4 r)+2 (p^2) (5 (q^2)+7 q r+3 (r^2))+2 p (4 (q^3)+9 (q^2) r+7 q (r^2)+2 (r^3))))) x y z+(-(b^4) (p-r) (((p+q+r))^2) (2 p+q+r)+(b^2) (c^2) (3 (p^4)+(p^3) (2 q-r)-7 p r (((q+r))^2)-2 r (((q+r))^3)+(p^2) ((q^2)-6 q r-7 (r^2)))+(c^4) (-(p^4)+r (((q+r))^3)+(p^3) (q+2 r)+p (((q+r))^2) (q+4 r)+(p^2) (2 (q^2)+7 q r+5 (r^2)))+(a^4) ((p^3) q+q r ((q^2)+3 q r+(r^2))+(p^2) (2 (q^2)+5 q r+(r^2))+p ((q^3)+6 (q^2) r+5 q (r^2)+2 (r^3)))+(a^2) ((b^2) (2 (p^4)+(p^3) (4 q+7 r)+p r (5 (q^2)+8 q r+(r^2))+(p^2) (2 (q^2)+10 q r+5 (r^2))+r (2 (q^3)+5 (q^2) r+2 q (r^2)-(r^3)))-2 (c^2) ((p^4)+(p^3) (q+3 r)+2 (p^2) ((q^2)+3 q r+(r^2))+q r ((q^2)+3 q r+2 (r^2))+p ((q^3)+6 (q^2) r+7 q (r^2)+(r^3))))) (y^2) z+(-(b^4) ((p^3) (q+3 r)+(p^2) ((q^2)+7 q r+2 (r^2))+(q^2) ((q^2)+4 q r+3 (r^2))+2 p q ((q^2)+5 q r+3 (r^2)))-(b^2) (c^2) ((p^4)+(p^3) (8 q+5 r)+6 (p^2) (2 (q^2)+2 q r+(r^2))+2 q ((q^3)+(q^2) r+q (r^2)+(r^3))+2 p (4 (q^3)+4 (q^2) r+3 q (r^2)+(r^3)))+(a^4) ((p^4)+(p^3) (3 q+2 r)+(p^2) (6 (q^2)+5 q r+(r^2))+2 p q (3 (q^2)+4 q r+2 (r^2))+q (3 (q^3)+6 (q^2) r+5 q (r^2)+2 (r^3)))+(c^4) ((p^4)+(p^3) (3 q+2 r)+(p^2) (6 (q^2)+5 q r+(r^2))+2 p q (3 (q^2)+4 q r+2 (r^2))+q (3 (q^3)+6 (q^2) r+5 q (r^2)+2 (r^3)))+(a^2) (-2 (c^2) ((p^4)+(p^3) (3 q+2 r)+(p^2) (6 (q^2)+5 q r+(r^2))+2 p q (3 (q^2)+4 q r+2 (r^2))+q (3 (q^3)+6 (q^2) r+5 q (r^2)+2 (r^3)))+(b^2) ((p^3) (4 q+5 r)+(p^2) (8 (q^2)+16 q r+9 (r^2))+2 q ((q^3)+(q^2) r+q (r^2)+(r^3))+2 p (4 (q^3)+8 (q^2) r+7 q (r^2)+2 (r^3))))) x (z^2)+(-(a^4) ((p^3) (2 q-r)+2 p (q^2) (2 q+3 r)+(p^2) (4 (q^2)+2 q r-(r^2))+(q^2) ((q^2)+4 q r+3 (r^2)))-(c^4) (2 (p^4)+q (((q+r))^2) (q+2 r)+(p^3) (4 q+3 r)+(p^2) (6 (q^2)+8 q r+(r^2))+2 p q (2 (q^2)+5 q r+3 (r^2)))-(b^4) ((p^4)+6 (p^3) (q+r)+q (((q+r))^2) (q+2 r)+(p^2) (7 (q^2)+14 q r+6 (r^2))+2 p (2 (q^3)+6 (q^2) r+5 q (r^2)+(r^3)))+(b^2) (c^2) (3 (p^4)+2 q (((q+r))^2) (q+2 r)+(p^3) (12 q+11 r)+2 (p^2) (7 (q^2)+12 q r+4 (r^2))+2 p (4 (q^3)+11 (q^2) r+8 q (r^2)+(r^3)))-(a^2) (-2 (c^2) ((p^4)+5 (p^2) q (q+r)+(p^3) (3 q+r)+p q (4 (q^2)+8 q r+3 (r^2))+q ((q^3)+4 (q^2) r+4 q (r^2)+(r^3)))+(b^2) (2 (p^4)+(p^3) (6 q+5 r)+3 (p^2) (4 (q^2)+6 q r+(r^2))+2 q ((q^3)+4 (q^2) r+4 q (r^2)+(r^3))+2 p (4 (q^3)+11 (q^2) r+7 q (r^2)+(r^3))))) y (z^2)+(((((a^2)-(c^2)))^2) q ((p^3)+2 p q (q+r)+q (((q+r))^2)+(p^2) (2 q+r))+(b^4) (p+q) ((p^3)+q (((q+r))^2)+(p^2) (4 q+3 r)+p (3 (q^2)+4 q r+(r^2)))-(b^2) ((a^2) ((p^3) r-2 (q^2) (((q+r))^2)+(p^2) (-4 (q^2)-2 q r+(r^2))-2 p q (3 (q^2)+4 q r+(r^2)))+(c^2) ((p^4)+2 (q^2) (((q+r))^2)+(p^3) (4 q+r)+2 (p^2) q (4 q+3 r)+2 p q (3 (q^2)+4 q r+(r^2))))) (z^3);
(* Van Aubel Cubic *)
QG2Cu1a=(-(1/4) (a+b-c) (a-b+c) (-a+b+c) (a+b+c) q-(1/4) (((-(a^2)+(b^2)+(c^2)))^2) q-(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((a^2)+(b^2)-(c^2)) r-(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (-(a^2)+(b^2)+(c^2)) r) (x^2) y+((1/4) (a+b-c) (a-b+c) (-a+b+c) (a+b+c) p+(1/4) (((-(a^2)+(b^2)+(c^2)))^2) p-(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((a^2)+(b^2)-(c^2)) r-(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (-(a^2)+(b^2)+(c^2)) r) x (y^2)-((1/2) ((a^2)+(b^2)-(c^2))+(1/2) (-(a^2)+(b^2)+(c^2))) ((-(a^2)+(b^2)+(c^2)) q+(1/2) ((a^2)+(b^2)-(c^2)) r+(1/2) (-(a^2)+(b^2)+(c^2)) r) (x^2) z+2 ((1/2) ((a^2)+(b^2)-(c^2))+(1/2) (-(a^2)+(b^2)+(c^2))) ((1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) p+(1/2) (-(a^2)+(b^2)+(c^2)) p-(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) r-(1/2) ((a^2)+(b^2)-(c^2)) r) x y z+((1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((a^2)+(b^2)-(c^2)) p+(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (-(a^2)+(b^2)+(c^2)) p-(1/4) (a+b-c) (a-b+c) (-a+b+c) (a+b+c) r-(1/4) ((((a^2)+(b^2)-(c^2)))^2) r) (y^2) z+((1/2) ((a^2)+(b^2)-(c^2))+(1/2) (-(a^2)+(b^2)+(c^2))) ((1/2) ((a^2)+(b^2)-(c^2)) p+(1/2) (-(a^2)+(b^2)+(c^2)) p+((a^2)+(b^2)-(c^2)) q) x (z^2)+((1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((a^2)+(b^2)-(c^2)) p+(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (-(a^2)+(b^2)+(c^2)) p+(1/4) (a+b-c) (a-b+c) (-a+b+c) (a+b+c) q+(1/4) ((((a^2)+(b^2)-(c^2)))^2) q) y (z^2);  (* 1st Perspective Square Cubic *)
QG2Cu1b=(-(1/4) (a+b-c) (a-b+c) (-a+b+c) (a+b+c) q-(1/4) (((-(a^2)+(b^2)+(c^2)))^2) q+(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((a^2)+(b^2)-(c^2)) r+(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (-(a^2)+(b^2)+(c^2)) r) (x^2) y+((1/4) (a+b-c) (a-b+c) (-a+b+c) (a+b+c) p+(1/4) (((-(a^2)+(b^2)+(c^2)))^2) p+(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((a^2)+(b^2)-(c^2)) r+(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (-(a^2)+(b^2)+(c^2)) r) x (y^2)-((1/2) ((a^2)+(b^2)-(c^2))+(1/2) (-(a^2)+(b^2)+(c^2))) ((-(a^2)+(b^2)+(c^2)) q+(1/2) ((a^2)+(b^2)-(c^2)) r+(1/2) (-(a^2)+(b^2)+(c^2)) r) (x^2) z+2 ((1/2) ((a^2)+(b^2)-(c^2))+(1/2) (-(a^2)+(b^2)+(c^2))) (-(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) p+(1/2) (-(a^2)+(b^2)+(c^2)) p+(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) r-(1/2) ((a^2)+(b^2)-(c^2)) r) x y z+(-(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((a^2)+(b^2)-(c^2)) p-(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (-(a^2)+(b^2)+(c^2)) p-(1/4) (a+b-c) (a-b+c) (-a+b+c) (a+b+c) r-(1/4) ((((a^2)+(b^2)-(c^2)))^2) r) (y^2) z+((1/2) ((a^2)+(b^2)-(c^2))+(1/2) (-(a^2)+(b^2)+(c^2))) ((1/2) ((a^2)+(b^2)-(c^2)) p+(1/2) (-(a^2)+(b^2)+(c^2)) p+((a^2)+(b^2)-(c^2)) q) x (z^2)+(-(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((a^2)+(b^2)-(c^2)) p-(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (-(a^2)+(b^2)+(c^2)) p+(1/4) (a+b-c) (a-b+c) (-a+b+c) (a+b+c) q+(1/4) ((((a^2)+(b^2)-(c^2)))^2) q) y (z^2);  (* 2nd Perspective Square Cubic *)