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Found problems: 1

2017 Bulgaria JBMO TST, 2
Tags: junior geometry , geometry
Let $k$ be the incircle of triangle $ABC$. It touches $AB=c, BC=a, AC=b$ at $C_1, A_1, B_1$, respectively. Suppose that $KC_1$ is a diameter of the incircle. Let $C_1A_1$ intersect $KB_1$ at $N$ and $C_1B_1$ intersect $KA_1$ at $M$. Find the length of $MN$.