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Equal Circumradii

Source: INAMO 2023 P1 (OSN 2023)

August 29, 2023

geometryIndonesiaIndonesia MOInamo

Problem Statement

An acute triangle

ABC

has

BC

as its longest side. Points

D,E

respectively lie on

AC,AB

such that

BA = BD

and

CA = CE

. The point

A'

is the reflection of

A

against line

BC

. Prove that the circumcircles of

ABC

and

A'DE

have the same radii.

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