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Conditional geo with incenters

Source: Bulgaria MO Regional round 2024, 12.1

February 13, 2024

geometry

Problem Statement

Let

ABC

be an acute triangle with midpoint

M

of

AB

. The point

D

lies on the segment

MB

and

I_1, I_2

denote the incenters of

\triangle ADC

and

\triangle BDC

. Given that

\angle I_1MI_2=90^{\circ}

, show that

CA=CB

.

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