MathDB

2008 JBMO Shortlist G11

Source: 2008 JBMO Shortlist G11

October 10, 2017

JBMOgeometry

Problem Statement

Consider

ABC

an acute-angled triangle with

AB \ne AC

. Denote by

M

the midpoint of

BC

, by

D, E

the feet of the altitudes from

B, C

respectively and let

P

be the intersection point of the lines

DE

and

BC

. The perpendicular from

M

to

AC

meets the perpendicular from

C

to

BC

at point

R

. Prove that lines

PR

and

AM

are perpendicular.

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