Problem #PRU-57809

Problems Geometry Plane geometry Plane transformations Parallel translation

Problem

Two circles of radius $R$ intersect at points $D$ and $B$ . Let $F$ and $G$ be the points of intersection of the middle perpendicular to the segment $B D$ with these circles lying on one side of the line $B D$ . Prove that $B D^{2} + F G^{2} = 4 R^{2}$ .

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