MathDB

AY = CZ wanted, circle and parallelogram (2019 Kyiv City MO Round2 8.4.1)

Source:

September 17, 2020

geometryparallelogramequal segments

Problem Statement

Through the vertices

A, B

of the parallelogram

ABCD

passes a circle that intersects for the second time diagonals

BD

and

AC

at points

X

and

Y

, respectively. The circumsccribed circle of

\vartriangle ADX

intersects diagonal

AC

for the second time at the point

Z

. Prove that

AY = CZ