QLP1: Miquel Point
The Miquel Point is the common point of the circumcircles of the 4 component triangles of the Reference Quadrilateral.
This point is also called the Steiner Point or Clifford Point.
He describes 134 circles of “more or less interest” through this point.
Coordinates:
1st CTcoordinate:
a^{2} m n/(m  n)
1st DTcoordinate:
b^{2}/(l^{2}n^{2})  c^{2}/(l^{2}m^{2})
Properties:

The Miquel Point QLP1 lies on these lines:
– QLCi3 (Miquel Circle),
– QLCi5 (Plücker Circle),
– QLCi6 (Dimidium Circle).
 QLP1 lies on QLCi2 (Ninepoint Circle of the QLDiagonal Triangle). See Ref32 as well as Ref11 (Hyacinthos Message # 12896 from Quang Tuan Bui).
 QLP1 lies on QLCu1 (QLQuasi Isogonal Cubic).
 QLP1 lies on QLQu1 (QLCardiode).
 QLP1 is the isogonal conjugate of the Infinity Point of the Newton line with respect to each of the four component triangles (see Ref4 page 41).
 The symmetric lines of the Steiner Line QLL2 in the 4 quadrilateral lines coincide at QLP1.
 QLP1 relates pairwise to all present line segments in the quadrilateral. It is the center of similarity of line segments Li^Lk . Li^Ll and Lj^Lk . Lj^Ll, where (i,j,k,l) ∊ (1,2,3,4). As a consequence triangles QLP1 . Li^Lk . Li^Ll and QLP1 . Lj^Lk . Lj^Ll are similar (see also Ref9).
 QLP1 is the perspector of the QLDiagonal Triangle and the Triangle formed by the 3 QLversions of QAP3 (GergonneSteiner Point).
 The ClawsonSchmidt Conjugate (QLTf1) is “centered” around QLP1.

The Miquel Point QLP1 of a Quadrilateral L1.L2.L3.L4 is the Isogonal Conjugate of the Infinity Point of the Trilinear Polar of the Isotomic Conjugate of the Trilinear Pole of Li wrt Triangle Lj.Lk.Ll, where (i,j,k,l) is any combination of {1,2,3,4}.
In short: MP = Ic(Ip(TPolar(It(TPole(Li))))).
(Francisco Javier García Capitán, Hyacinthos message #21271(Ref11), November 5, 2012)
 QLP1 is the QATf2 image (Involutary Conjugate) of QGP16 (Eckart Schmidt, November 26, 2012).
 QLP1 lies on the Polars (see Ref13, Polar) of QLP2, QLP7, QLP9 wrt QLCo1.
 Let ABCD be a Component Quadrigon of the Reference Quadrilateral and let P be its Miquel Point. If m is the distance between the midpoints of the diagonals of ABCD, then PA/(AB*AD) = PB/(BA*BC)=PC/(CB*CD)=PD/(DA*DC)=1/(2*m) (see Ref11, Hyacinthos message # 9086).

Let Ti = Triangle formed by the 3 lines Lij, Lik, Lil ((i,j,k,l) ∈ (1,2,3,4)) where Lmn = Line perpendicular to Ln at intersection point Lm^Ln. The 4 triangles Ti (i=1,2,3,4) have one common point, being QLP1. Moreover the circumcenters of the 4 triangles Ti (i=1,2,3,4) lie on QLCi3. Found by Antreas P. Hatzipolakis, see Ref33, Anopolis messages # 466,467.
 The QAOrthopole (QATf3) of QLP1 is a point on the Newton Line QLL1.
 The QAMöbius Conjugate (QATf4) of QLP1 is QGP5.

QLP1 lies on the polar of QGP16 wrt QGCo2 (and invers) (Eckart Schmidt, October 9, 2013). See Ref34, QFG # 286.
 The QATriple Triangle of QLP1 is Perspective and Cyclologic wrt all QAComponent Triangles (Ref34, QFG#977 by Seiichi Kirikami). See QATr1.
 The QATriple Triangle of QLP1 is Orthologic wrt the Triple Triangles of QGP7, QGP9 and QLP6. See QATr1.
 The reflections of QLP1 in the 4 basic lines of the Reference Quadrilateral lie on QLL2. See Ref34, Seiichi Kirikami, QFG message # 1091.
 The reflections of QLL2 in the 4 basic lines of the Reference Quadrilateral concur in QLP1. See Ref34, Seiichi Kirikami, QFG message # 1095.
 The line through the intersection point of Li and Lj (i,j=1,2,3,4) and through the intersection point of the reflected lines of QLL3 in Li and Lj passes through QLP1. See Ref34, Seiichi Kirikami, QFG message # 1096.
 The Orthopole of ANY line through QLP1 wrt ANY Component Triangle of the Reference Quadrilateral lies on QLL3. See Ref33, Anopolis # 637.