MathDB

Albanian TST 2014 3rd problem

Source:

April 21, 2014

geometry proposedgeometry

Problem Statement

From the point

P

outside a circle

\omega

with center

O

draw the tangents

PA

and

PB

where

A

and

B

belong to

\omega

.In a random point

M

in the chord

AB

we draw the perpendicular to

OM

, which intersects

PA

and

PB

in

C

and

D

. Prove that

M

is the midpoint

CD

.

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