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Intersection lies on fixed circle

Source: Own. IMO 2022 Malaysian Training Camp 1

February 27, 2022

geometry

Problem Statement

A pentagon

B,C,D,E

is such that

ABCD

is cyclic,

BE\parallel CD

, and

DB=DE

. Let us fix the points

B,C,D,E

and vary

A

on the circumcircle of

BCD

. Let

P=AC\cap BE

, and

Q=BC\cap DE

.
Prove that the second intersection of circles

(ABE)

and

(PQE)

lie on a fixed circle.

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