Question 191
In the quadrilateral $ABCD$ with $\angle ABC = \angle CDA = 90^\circ$. Let us denote $P = AC \cap BD$, $Q = AB \cap CD$, $R = AD \cap BC$. Let $l$ be the midline of the triangle $PQR$ parallel to $QR$. Prove that the circumcircle of the triangle formed by the lines $AB, AD$ and $l$ is tangent to the circumcircle of the triangle formed by the lines $CD, CB$ and $l$.
(Fedir Yudin)
**Fig. 15**
(Fedir Yudin)
**Fig. 15**