2

Part of 2015 JBMO Shortlist

Problems(1)

2015 JBMO Shortlist G2

Source: 2015 JBMO Shortlist G2

{P}

is outside the circle

{\Omega}

. Two tangent lines, passing from the point

{P}

touch the circle

{\Omega}

{A}

{B}

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

intersects the circle

{\Omega}

{C}

{PC}

intersects again the circle

{\Omega}

{D}

. Prove that the lines

{AD}

{BP}

are parallel.
(Moldova)