Problem

Source: Sharygin Geometry Olympiad Correspondence Round 2017 P-4 (Grade-8)

Tags: geometry



A triangle $ABC$ is given. Let $C\ensuremath{'}$ be the vertex of an isosceles triangle $ABC\ensuremath{'}$ with $\angle C\ensuremath{'} = 120^{\circ}$ constructed on the other side of $AB$ than $C$, and $B\ensuremath{'}$ be the vertex of an equilateral triangle $ACB\ensuremath{'}$ constructed on the same side of $AC$ as $ABC$. Let $K$ be the midpoint of $BB\ensuremath{'}$ Find the angles of triangle $KCC\ensuremath{'}$. Proposed by A.Zaslavsky