A Quadrilateral with Balanced Areas

★ 6/10plane geometry Law of Cosines Triangle Geometry

Problem

Convex quadrilateral $ABCD$ has side lengths $AB = CD = 10$ , $BC = 14$ , and $AD = 2\sqrt{65}$ . Its diagonals intersect at point $P$ , and 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 $ABCD$ .

Answer

Solution

Difficulty	6/10
Topics	plane geometry, Law of Cosines, Triangle Geometry

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