62. On a plane, there are two lines intersecting at point $O$, and two points $A$ and $B$. Denote the bases of the perpendiculars dropped from $A$ to the given lines as $M$ and $N$, and the bases of the perpendiculars dropped from $B$ as $K$ and $L$. Find the angle between the lines $M N$ and $K L$, if $\widehat{A O B}=\alpha \leqslant 90^{\circ}$.
62. Note that points $A, M, N$ and $O$ lie on the same circle (Fig. 11). Therefore, $\widehat{N M O}=\widehat{O A N}=90^{\circ}-\widehat{A O N}$. This means that when $O A$ is rotated around $O$

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Fig. 11. by an angle $\varphi$, the line $N M$ will also rotate by the same angle $\varphi$ (in the opposite direction), and when $A$ moves along the line $O A$, the line $N M$ moves parallel to itself. From this, it follows that the required angle is $\alpha$.