Math: Geometry Problem 1110: Right Triangle, External Squares, Catheti, Cathetus, Angle Bisector, 45 Degree, Internal Square. Level: High School, College

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The figure shows a right triangle ABC with the angle bisector BQ and the external squares ABDE and BCFG. AF meets BC at M and CE meets AB at N. Prove that BMQN is a square

$Geometry Problem 1110 Right Triangle, External Squares, Catheti, Cathetus, Angle Bisector, Internal Square$