2019 USAJMO Problems/Problem 3

Problem

$(*)$ Let $ABCD$ be a cyclic quadrilateral satisfying $AD^2+BC^2=AB^2$ . The diagonals of $ABCD$ intersect at $E$ . Let $P$ be a point on side $\overline{AB}$ satisfying $\angle APD=\angle BPC$ . Show that line $PE$ bisects $\overline{CD}$ .

Solution

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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2019 USAJMO (Problems • Resources)
Preceded by Problem 2	Followed by Problem 4
1 • 2 • 3 • 4 • 5 • 6
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2019 USAJMO Problems/Problem 3

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