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angle chasing, AC=1/2(AB + BC) bisector, midpoints (2014 Kyiv City MO 10.4.1)

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August 6, 2020
geometryanglesangle bisector

Problem Statement

In the triangle ABCABC the side AC=12(AB+BC)AC = \tfrac {1} {2} (AB + BC) , BLBL is the bisector ∠ABC\angle ABC, K,  MK, \, \, M - the midpoints of the sides ABAB and BCBC, respectively. Find the value ∠KLM\angle KLM if ∠ABC=β\angle ABC = \beta
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