MathDB

2015 JBMO Shortlist G2

Source: 2015 JBMO Shortlist G2

October 8, 2017

geometryJBMO

Problem Statement

The point

{P}

is outside the circle

{\Omega}

. Two tangent lines, passing from the point

{P}

touch the circle

{\Omega}

at the points

{A}

and

{B}

. The median

{AM \left(M\in BP\right)}

intersects the circle

{\Omega}

at the point

{C}

and the line

{PC}

intersects again the circle

{\Omega}

at the point

{D}

. Prove that the lines

{AD}

and

{BP}

are parallel.
(Moldova)

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