MathDB

Pentagon geo from ARO

Source: ARO 2021 10.8

April 20, 2021

geometry

Problem Statement

Given is a cyclic pentagon

ABCDE

, inscribed in a circle

k

. The line

CD

intersects

AB

and

AE

in

X

and

Y

respectively. Segments

EX

and

BY

intersect again at

P

, and they intersect

k

in

Q

and

R

, respectively. Point

A'

is reflection of

A

across

CD

. The circles

(PQR)

and

(A'XY)

intersect at

M

and

N

. Prove that

CM

and

DN

intersect on

(PQR)

.

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