Question 105
In the triangle $ABC$ denote $D$ point of contact of side $BC$ with the incircle. The incircle of the triangle $ABD$ is tangent to sides $AB$ and $BD$ at points $K$ and $L$. The incircle of the triangle $ADC$ is tangent to sides $DC$ and $AC$ at points $M$ and $N$. Prove that points $K, L, M, N$ lie on the same circle.