Question 5
Inside the triangle $ABC$ there exists a point $O$ such that $\angle BOC = 90^\circ - \angle BAC$. The rays $BO$ and $CO$ intersect the sides $AC$ and $AB$ at the points $K$ and $L$ respectively. The points $K_1$ and $L_1$ are selected on the segments $LC$ and $BK$ respectively, so that $BK_1 = K_1K$ and $CL_1 = L_1L$. Let $M$ be the midpoint of the side $BC$. Prove that $\angle K_1ML_1$ is a right angle.
(Anton Trygub)
**Figure 18**
(Anton Trygub)
**Figure 18**