3. $\mathrm{ABCD}$ is a trapezoid with bases $A D=15$ and $\mathrm{BC}=10$. $O$ is one of the intersection points of the circles constructed on the lateral sides of the trapezoid as diameters, and this point lies inside the trapezoid. Triangle $B C M$ is constructed on side $B C$ on the external side relative to the trapezoid and is similar to triangle $A D O$ (the vertices of the triangles are listed in the order in which they correspond to each other). Line $O M$ intersects the bases $B C$ and $A D$ at points $K$ and $L$ respectively. It is known that $O K=4, O L=9$. Find the smallest possible value of the length of segment $B K$.
Answer: 4

## Examples of answer notations:

$1 / 4$

0.25

10