QG-2P2: Endpoints 3^rd QA-diagonal

In a Quadrigon (system of 4 consecutive points P1, P2, P3, P4) the Diagonal Triangle of a Quadrangle (system of 4 points unrestricted) can be seen as a triangle with these vertices:

• the Diagonal Crosspoint (QG-P1) representing the 1^st vertex,
• the Endpoints at the QA-3^rd Diagonal representing the 2^nd and 3^rd vertice, which are QG-2P2a and QG-2P2b.

When the Quadrigon vertices are P1, P2, P3, P4 in this order, then:

• QG-P1 = intersection point P1.P3 ^ P2.P4
• QG-2P2a = intersection point P1.P2 ^ P3.P4
• QG-2P2b = intersection point P1.P4 ^ P2.P3.

CT-coordinates QG-2P2a/b in 1^st QA-Quadrigon:

QG-2P2a:(p : q : 0)

QG-2P2b: (0 : q : r)

CT-coordinates QG-2P2a/b in 1^st QL-Quadrigon:

QG-2P2a:(0 : 1 : 0)

QG-2P2b: (n : 0 : -l)

DT-coordinates QG-2P2a/b in 1^st QA-Quadrigon:

QG-2P2a:(0 : 0 : 1)

QG-2P2b: (1 : 0 : 0)

DT-coordinates QG-2P2a/b in 1^st QL-Quadrigon:

QG-2P2a:(n : 0 : l)

QG-2P2b: (n : 0 : -l)

Properties

• QG-2P2a and QG-2P2b are collinear with QG-P2, QG-P3, QG-2P3a/b.
• QG-2P2a and QG-2P2b are each other’s Reflection in QG-P2.
• QG-2P2a and QG-2P2b define the line segment which is the diameter of QG-Ci1 (QA-DT-Thales Circle).
• Let L2a and L2b be the lines through QG-2P2a and QG-2P2b parallel to QG-P1.QL-P13. Let L3a, L3b and L3c be the sidelines of the QL-Diagonal Triangle, L3c being the 3^rd diagonal QG-L1. The pairs of triangles (L3a,L3c,L2a) and (L3b,L3c,L2a) as well as (L3a,L3c,L2b) and (L3b,L3c,L2b) have equal areas. See [50], ADGEOM #2380/2382/2383, where L2a and L2b are called area equalizers.

Estimated human page views: 501