MathDB

Geo problem

Source: Baltic Way 1995

November 29, 2010

geometry unsolvedgeometry

Problem Statement

Let

M

be the midpoint of the side

AC

of a triangle

ABC

and let

H

be the foot of the altitude from

B

. Let

P

and

Q

be orthogonal projections of

A

and

C

on the bisector of the angle

B

. Prove that the four points

H,P,M

and

Q

lie on the same circle.

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