MathDB

Incircle geo with angle conditions

Source: 239 MO 2024 J4

May 22, 2024

geometry

Problem Statement

Let

I

be the incenter of a triangle

ABC

. The points

\angle IAY=\angle ICA

lie on the prolongations of the lines

IB, IC

after

I

so that

\angle IAX=\angle IBA

and

\angle IAY=\angle ICA

. Show that the line through the midpoints of

IA

and

XY

passes through the circumcenter of

ABC

.

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