MathDB
Circles and angles

Source: Baltic Way 2015

November 8, 2015
geometry

Problem Statement

A circle passes through vertex BB of the triangle ABCABC, intersects its sides AB AB and BCBC at points KK and LL, respectively, and touches the side AC AC at its midpoint MM. The point NN on the arc BLBL (which does not contain KK) is such that ∠LKN=∠ACB\angle LKN = \angle ACB. Find ∠BAC\angle BAC given that the triangle CKNCKN is equilateral.
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