Two circles $(C_1$ with radius $r_1$, and $C_2$ with radius $r_2$) are having the same centre. $P_1$ and $P_2$ are two distinct points lying on the circumference of $C_1$. The length of line $P_1P_2$ is $l$ units and it is tangent to $C_2$.
How can I express $r_2$ in terms of $r_1$ and $l$?
If $P_1P_2$ is tangent to the innermost circle, then the distance from the center to $P_1P_2$ is $r_2.$ You know that the distance from the center to either $P_1$ or $P_2$ is $r_1.$ You only need to use the Pythagorean theorem to find the value you need.