A circle with a given radius is to be constructed, which passes through a given point $A$, if the length of the tangent $(l)$ drawn from a given point $B$ is also known!





Construct a circle with a given radius that passes through a given point $A$, if the length of the tangent $(l)$ drawn from a given point $B$ is known!
The geometric place of the centers of circles with radius $r$ passing through point $A$ is the circle $k_{1}$, whose center is $A$ and radius is $r$.

The geometric place of the centers of circles that satisfy the second condition is the circle $k_{2}$, whose center is $B$ and radius is equal to the hypotenuse of a right triangle with legs $l$ and $r$. (In our diagram: $BM = l, MN = r$), so the radius of $k_{2}$ is $BN = \sqrt{l^2 + r^2}$.

The circles that satisfy both conditions are the common points of circles $k_{1}$ and $k_{2}$.

The number of solutions: $2, 1, 0$, depending on whether

$$
AB \oint r + \sqrt{l^2 + r^2}
$$