MathDB

Center and midpoint

Source: Lusophon MO

February 17, 2018

geometry

Problem Statement

The circle

\omega_1

intersects the circle

\omega_2

in the points

A

and

B

, a tangent line to this circles intersects

\omega_1

and

\omega_2

in the points

E

and

\omega_1

respectively. Suppose that

A

is inside of the triangle

BEF

, let

H

be the orthocenter of

BEF

and

M

is the midpoint of

BH

. Prove that the centers of the circles

\omega_1

and

\omega_2

and the point

M

are collinears.

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