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2023 Iran MO 2nd round P6

Source: 2023 Iran MO

May 17, 2023

geometry

Problem Statement

6. Circles

W_{1}

and

W_{2}

with equal radii are given. Let

P

,

Q

be the intersection of the circles. points

B

and

C

are on

W_{1}

and

W_{2}

such that they are inside

W_{2}

and

W_{1}

respectively. Points

X

,

Y

\neq

P

are on

W_{1}

and

W_{2}

respectively, such that

\angle{BPQ}=\angle{BYQ}

and

\angle{CPQ}=\angle{CXQ}

.Denote by

S

as the other intersection of

(YPB)

and

(XPC)

. Prove that

QS,BC,XY

are concurrent.

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