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angles in right triangle, with perpendicular bisectors

Source: IGO Elementary 2016 4

July 22, 2018
geometryright triangleperpendicular bisector

Problem Statement

In a right-angled triangle ABCABC (∠A=90o\angle A = 90^o), the perpendicular bisector of BCBC intersects the line ACAC in KK and the perpendicular bisector of BKBK intersects the line ABAB in LL. If the line CLCL be the internal bisector of angle CC, find all possible values for angles BB and CC.
by Mahdi Etesami Fard
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