MathDB

Circles centred at vertices of regular pentagon

Source: Canada Repêchage 2021/3 CMOQR

March 30, 2021

Canadarepechagegeometrypentagon

Problem Statement

ABCDE

is a regular pentagon. Two circles

C_1

and

C_2

are drawn through

B

with centers

A

and

C

respectively. Let the other intersection of

C_1

and

C_2

be

P

. The circle with center

P

which passes through

E

and

D

intersects

C_2

at

X

and

AE

at

Y

. Prove that

AX = AY

.

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