MathNet 2019-part-07 — 184 problems (EN–VI) Question 92

Let $ABCD$ be a parallelogram. The circle through $A$ and $D$ intersects the lines $AB$, $BD$, $AC$ and $CD$ in points $B_1$, $B_2$, $C_1$ and $C_2$ respectively. Let $K$ be the intersection point of the lines $B_1B_2$ and $C_1C_2$. Prove that $K$ is equidistant from the lines $AB$ and $CD$.



Fig. 41