MathDB

Let

ABC

be a triangle, let

B_{1}

be the midpoint of the side

AB

and

C_{1}

the midpoint of the side

AC

. Let

P

be the point of intersection, other than

A

, of the circumscribed circles around the triangles

ABC_{1}

and

AB_{1}C

. Let

P_{1}

be the point of intersection, other than

A

, of the line

AP

with the circumscribed circle around the triangle

AB_{1}C_{1}

. Prove that

2AP=3AP_{1}

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