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A and P equidistant from incenter

Source: KöMaL A 726

June 12, 2018

geometryincenter

Problem Statement

In triangle

ABC

with incenter

I

, line

AI

intersects the circumcircle of

ABC

at

S\ne A

. Let the reflection of

I

with respect to

BC

be

J

, and suppose that line

SJ

intersects the circumcircle of

ABC

for the second time at point

P\ne S

. Show that

AI=PI.

József Mészáros

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