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Construct the center and the radius of the circle-[ILL 1977]

Source:

January 11, 2011
geometry proposedgeometry

Problem Statement

Given an isosceles triangle ABCABC with a right angle at C,C, construct the center MM and radius rr of a circle cutting on segments AB,BC,CAAB, BC, CA the segments DE,FG,DE, FG, and HK,HK, respectively, such that ∠DME+∠FMG+∠HMK=180∘\angle DME + \angle FMG + \angle HMK = 180^\circ and DE:FG:HK=AB:BC:CA.DE : FG : HK = AB : BC : CA.
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