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AM = LC wanted, BL = AB, <AML = <BCA (2015 Kyiv City MO Round2 7.4 8.4 9.4.1)

Source:

September 3, 2020
geometryequal segmentsangle bisectorequal angles

Problem Statement

In the acute triangle ABCABC the side BC>ABBC> AB, and the angle bisector BL=ABBL = AB. On the segment BLBL there is a point MM, for which ∠AML=∠BCA\angle AML = \angle BCA. Prove that AM=LCAM = LC.
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