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2019 USAMO Problems/Problem 2

Revision as of 23:10, 19 April 2019 by Superram (talk | contribs) (Created page with "==Problem== Let <math>ABCD</math> be a cyclic quadrilateral satisfying <math>AD^2 + BC^2 = AB^2</math>. The diagonals of <math>ABCD</math> intersect at <math>E</math>. Let <ma...")
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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

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See also

2019 USAMO (Problems • Resources)
Preceded by
Problem 1 		Followed by
Problem 3
1 • 2 • 3 • 4 • 5 • 6
All USAMO Problems and Solutions
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