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Bosnia and Herzegovina JBMO TST 2013 Problem 3

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2013

September 16, 2018

geometryincircleangle bisector

Problem Statement

Let

M

and

N

be touching points of incircle with sides

AB

and

AC

of triangle

ABC

, and

P

intersection point of line

MN

and angle bisector of

\angle ABC

. Prove that

\angle BPC =90 ^{\circ}