A Quadrilateral of Centroids

★ 6/10plane geometry analytic geometry Triangle Geometry

Problem

A square $ABCD$ has side length $30$ . A point $P$ inside the square satisfies $AP=12$ and $BP=26$ . The centroids of $\triangle ABP$ , $\triangle BCP$ , $\triangle CDP$ , $\triangle DAP$ are the vertices of a convex quadrilateral. Find the area of that quadrilateral.

Answer

Solution

Difficulty	6/10
Topics	plane geometry, analytic geometry, Triangle Geometry

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