MathDB

Lots of cyclic quadrilaterals

Source: MEMO 2015, problem I-3.

August 27, 2015

geometrycyclic quadrilateralcircumcircleAngle Chasing

Problem Statement

Let

ABCD

be a cyclic quadrilateral. Let

E

be the intersection of lines parallel to

AC

and

BD

passing through points

B

and

A

, respectively. The lines

EC

and

ED

intersect the circumcircle of

AEB

again at

F

and

G

, respectively. Prove that points

C

D

F

, and

G

lie on a circle.