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Moldova tst egmo 2017

Source: MDA TST for egmo 2017, problem 2

April 26, 2017

geometry

Problem Statement

Let us denote the midpoint of

AB

with

O

. The point

C

, different from

A

and

B

is on the circle

\Omega

with center

O

and radius

OA

and the point

D

is the foot of the perpendicular from

C

to

AB

. The circle with center

C

and radius

CD

and

\omega

intersect at

M

,

N

. Prove that

MN

cuts

CD

in two equal segments.

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