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2018 AIME II Problems/Problem 12

Revision as of 08:37, 24 March 2018 by P groudon (talk | contribs) (Created page with "==Problem== Let <math>ABCD</math> be a convex quadrilateral with <math>AB = CD = 10</math>, <math>BC = 14</math>, and <math>AD = 2\sqrt{65}</math>. Assume that the diagonals...")
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Problem

Let $ABCD$ be a convex quadrilateral with $AB = CD = 10$, $BC = 14$, and $AD = 2\sqrt{65}$. Assume that the diagonals of $ABCD$ intersect at point $P$, and that the sum of the areas of triangles $APB$ and $CPD$ equals the sum of the areas of triangles $BPC$ and $APD$. Find the area of quadrilateral $ABCD$.

2018 AIME II (Problems • Answer Key • Resources)
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Problem 11 		Followed by
Problem 13
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All AIME Problems and Solutions

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