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BK = 2DC wanted, < ABC = < KAD = < AKD, < CAB = 90^o

Source: 2010 Grand Duchy of Lithuania, Mathematical Contest p4 (Baltic Way TST)

October 2, 2020
geometryequal anglesright triangleequal segments

Problem Statement

In the triangle ABCABC angle CC is a right angle. On the side ACAC point DD has been found, and on the segment BDBD point K has been found such that ∠ABC=∠KAD=∠AKD\angle ABC = \angle KAD = \angle AKD. Prove that BK=2DCBK = 2DC.
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