## 22476Isogonal Conjugates - NPC - Radical Axis

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• Jun 29, 2014
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Let ABC be a triangle, P,P* two isogonal conugate points
and PaPbPc, P*aP*bP*c the pedal triangles of P, P*, resp.

Denote:

Ab = the orthogonal projection of Pa on AC
A2 = the reflection of A in Ab
(= the other than A intersection of the circle (Pa, PaA) and AC)

Ac = the orthogonal projection of Pa on AB
A3 = the reflection of A in Ac
(= the other than A intersection of the circle (Pa, PaA) and AB)

(Na) = the NPC of AA2A3

A*b = the orthogonal projection of P*a on AC
A*2 = the reflection of A in A*b
(= the other than A intersection of the circle (P*a, P*aA) and AC)

A*c = the orthogonal projection of P*a on AB
A*3 = the reflection of A in A*c
(= the other than A intersection of the circle (P*a, P*aA) and AB)

(N*a) = the NPC of AA*2A*3

Ra = the radical axis of (Na) and (N*b)

Similarly Rb and Rc.

The Ra,Rb,Rc are concurrent.
The parallels to Ra,Rb,Rc through A,B,C, resp. concur at a fixed point
[X(74)]

Antreas