MathDB

CX=CY wanted, intersecting circles, # (2021 Kyiv City MO 10.3 11.3)

Source:

February 15, 2021

geometrycirclesequal segmentsparallelogram

Problem Statement

Circles

\omega_1

and

\omega_2

with centers at points

O_1

and

O_2

intersect at points

A

and

B

. A point

C

is constructed such that

AO_2CO_1

is a parallelogram. An arbitrary line is drawn through point

A

, which intersects the circles

\omega_1

and

\omega_2

for the second time at points

X

and

Y

, respectively. Prove that

CX = CY

.
(Oleksii Masalitin)