IMO 2006 Shortlist G3

Let ABCDE be a convex pentagon such that ∠BAC = ∠CAD = ∠DAE and ∠ABC = ∠ACD = ∠ADE. The diagonals BD and CE meet at P. P...

imomathematicsolympiadshortlistgeometry

IMO 2006 Shortlist G3

Category: Geometry

Problem

Let ABCDE be a convex pentagon such that ∠BAC = ∠CAD = ∠DAE and ∠ABC = ∠ACD = ∠ADE. The diagonals BD and CE meet at P. Prove that the line AP bisects the side CD. (USA)