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PQ // AC wanted, cyclic ABCD with AB=BC

Source: 2021 Dutch BxMO TST p1

December 28, 2021

geometryparallelcyclic quadrilateral

Problem Statement

Given is a cyclic quadrilateral

ABCD

with

|AB| = |BC|

. Point

E

is on the arc

CD

where

A

and

B

are not on. Let

P

be the intersection point of

BE

and

CD

, let

Q

be the intersection point of

AE

and

BD

. Prove that

PQ \parallel AC

.

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