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Two congruent triangles form a cyclic quad

Source: 2021 Thailand Online MO P7 (Mock TMO contest)

April 6, 2021

geometrycongruent triangles

Problem Statement

Let

ABC

be an acute triangle. Construct a point

X

on the different side of

C

with respect to the line

AB

and construct a point

Y

on the different side of

B

with respect to the line

AC

such that

BX=AC

,

CY=AB

, and

AX=AY

. Let

A

be the reflection of

A

across the perpendicular bisector of

X

. Suppose that

X

and

Y

lie on different sides of the line

AA'

, prove that points

A

,

A'

,

X

, and

Y

lie on a circle.

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