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PA' and B'C' intersect on A-median

Source: Spain MO 2010

February 11, 2011

geometryincentergeometry proposed

Problem Statement

In a triangle

ABC

, let

P

be a point on the bisector of

\angle BAC

and let

A',B'

and

C'

be points on lines

BC,CA

and

AB

respectively such that

PA'

is perpendicular to

BC,PB'\perp AC

, and

PC'\perp AB

. Prove that

PA'

and

B'C'

intersect on the median

AM

, where

M

is the midpoint of

BC

.

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