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Prove that intersection of two circumcircle lie on a line

Source: 2022 Thailand Online MO P2

April 4, 2022

geometrycircumcircle

Problem Statement

Let

ABCD

be a trapezoid such that

AB \parallel CD

and

AB > CD

. Points

X

and

Y

are on the side

AB

such that

XY = AB-CD

and

X

lies between

A

and

Y

. Prove that one intersection of the circumcircles of triangles

AYD

and

BXC

is on line

CD

.

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