Question

If $13,18$ are radii of two concentric circles and $AB$ is the diameter of bigger circle and $BD$ is tangent to smaller circle touching at $D$. Then find $AP$.

Answer 1

$\begin{array}{c}Letradii=18=AO=OB\\ Smallerradii=OD=13\\ \angle ODB={90}^0\left(\tan gent\perp radius\right)\\ \angle APB={90}^0\left(angleinsemicircle={90}^0\right)\\ In\Delta ABP\&\Delta OBD\\ \angle APB=\angle ODB\\ \angle ABP=\angle OBD\\ \therefore \Delta ABP\sim \Delta OBD\left(AA-similarity\right)\\ \frac{AP}{OD}=\frac{AB}{OB}\\ AP=\frac{18\times 2}{18}\times 13=26cm\end{array}$