Dynamic Geometry 1478: Reuschle-Terquem Theorem, Concurrent Cevians, Triangle, Circumcircle, Secant line, Cyclocevian, Step-by-step Illustration

In a triangle ABC the cevians AA1,BB1,CC1 are concurrent at P1. The circumcircle of triangle A1B1C1 intercept the sides at A2,B2,C2. Prove that the cevians AA2,BB2,CC2 are concurrent at a point P2 known as cyclocevian conjugate of P1. See dynamic diagram.

Weisstein, Eric W. "Cyclocevian Conjugate." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CyclocevianConjugate.html

See solution below

Static Diagram of Reuschle-Terquem Theorem

Problem 1478 Reuschle-Terquem Theorem, Concurrent Cevians, Triangle, Circumcircle, Step-by-step Illustration, iPad Apps

Poster of the Reuschle-Terquem Theorem using iPad Apps

Dynamic Geometry 1478: Reuschle-Terquem Theorem, Concurrent Cevians, Triangle, Circumcircle, Step-by-step Illustration Using GeoGebra, iPad Apps

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