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2013 JBMO Shortlist G1

Source: 2013 JBMO Shortlist G1

October 8, 2017

geometryJBMO

Problem Statement

Let

{AB}

be a diameter of a circle

{\omega}

and center

{O}

,

{OC}

a radius of

{\omega}

perpendicular to

AB

,

{M}

be a point of the segment

\left( OC \right)

. Let

{N}

be the second intersection point of line

{AM}

with

{\omega}

and

{P}

the intersection point of the tangents of

{\omega}

at points

{N}

and

{B.}

Prove that points

{M,O,P,N}

are cocyclic.
(Albania)

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