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a right-angled triangle can be constructed from the segments AK, CM,MK

Source: 2010 Oral Moscow Geometry Olympiad grades 8-9 p4

August 16, 2020
geometrytriangle inequalityright triangleisosceles

Problem Statement

An isosceles triangle ABCABC with base ACAC is given. Point HH is the intersection of altitudes. On the sides ABAB and BCBC, points MM and KK are selected, respectively, so that the angle KMHKMH is right. Prove that a right-angled triangle can be constructed from the segments AK,CMAK, CM and MKMK.