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Five points [CMO 2018 - P2]

Source: 2018 Canadian Mathematical Olympiad - P2

March 31, 2018

geometry

Problem Statement

Let five points on a circle be labelled

A, B, C, D

, and

E

in clockwise order. Assume

AE = DE

and let

P

be the intersection of

AC

and

BD

. Let

Q

be the point on the line through

A

and

B

such that

A

is between

B

and

Q

and

AQ = DP

Similarly, let

R

be the point on the line through

C

and

D

such that

D

is between

C

and

R

and

DR = AP

. Prove that

PE

is perpendicular to

QR

.

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