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Iberoamerican Olympiad 2013 - Problem 2

Source: http://oim2013.opm.org.pa/pdfs/examen_pt.pdf

August 13, 2014

geometrypower of a pointradical axisgeometry proposed

Problem Statement

Let

X

and

Y

be the diameter's extremes of a circunference

\Gamma

and

N

be the midpoint of one of the arcs

XY

of

\Gamma

. Let

A

and

B

be two points on the segment

XY

. The lines

NA

and

NB

cuts

\Gamma

again in

C

and

D

, respectively. The tangents to

\Gamma

at

C

and at

D

meets in

P

. Let

M

the the intersection point between

XY

and

NP

. Prove that

M

is the midpoint of the segment

AB

.

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