MathDB

Intersections and a vertex form a cyclic quadrilateral

Source: 2021 Centroamerican and Caribbean Mathematical Olympiad, P2

August 11, 2021

geometrycircumcirclecyclic quadrilateral

Problem Statement

Let

ABC

be a triangle and let

\Gamma

be its circumcircle. Let

D

be a point on

AB

such that

CD

is parallel to the line tangent to

\Gamma

at

A

. Let

E

be the intersection of

CD

with

\Gamma

distinct from

C

, and

F

the intersection of

BC

with the circumcircle of

\bigtriangleup ADC

distinct from

C

. Finally, let

G

be the intersection of the line

AB

and the internal bisector of

\angle DCF

. Show that

E,\ G,\ F

and

C

lie on the same circle.

Back to Problems View on AoPS