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Mnp right triangle

Source: 14-th Iranian Mathematical Olympiad 1996/1997

October 17, 2005
trigonometrygeometry proposedgeometry

Problem Statement

Let NN be the midpoint of side BCBC of triangle ABCABC. Right isosceles triangles ABMABM and ACPACP are constructed outside the triangle, with bases ABAB and ACAC. Prove that △MNP\triangle MNP is also a right isosceles triangle.
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