MathDB

2019 IGO Intermediate P1

Source: 6th Iranian Geometry Olympiad (Intermediate) P1

September 20, 2019

IGOIrangeometryparallelogram

Problem Statement

Two circles

\omega_1

and

\omega_2

with centers

O_1

and

O_2

respectively intersect each other at points

A

and

B

, and point

O_1

lies on

\omega_2

. Let

P

be an arbitrary point lying on

\omega_1

. Lines

BP, AP

and

O_1O_2

cut

\omega_2

for the second time at points

X

,

Y

and

C

, respectively. Prove that quadrilateral

XPYC

is a parallelogram.
Proposed by Iman Maghsoudi

Back to Problems View on AoPS