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Italian WinterCamps test07 Problem4

Source: ISL 2006, G3, VAIMO 2007/5

January 29, 2007
geometrycircumcirclepentagonIMO Shortlist

Problem Statement

Let ABCDE ABCDE be a convex pentagon such that \angle BAC \equal{} \angle CAD \equal{} \angle DAE\qquad \text{and}\qquad \angle ABC \equal{} \angle ACD \equal{} \angle ADE. The diagonals BDBD and CECE meet at PP. Prove that the line APAP bisects the side CDCD.
Proposed by Zuming Feng, USA
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