MathNet 2023-part-07 — 187 problems (EN–VI) Question 13

Let $K$ be the midpoint of the median $AM$ of the triangle $ABC$. On the side $AB$ there is a point $X$ such that $\angle KXM = \angle ACB$ and $AX \gt BX$, and on the side $AC$ there is a point $Y$ such that $\angle KYM = \angle ABC$ and $AY \gt CY$. Prove that the points $B, X, C, Y$ lie on the same circle.

(Mykhailo Shtandenko)


Figure 19