Question

$\overline{OC}$ and $\overline{OD}$ are distinct radii of $⨀(0,r)$ and $\overline{OC}\perp \overline{OD}$. Tangents drawn from $C$ and $D$ intersect each other in $A$. If $OA=5\sqrt{2}$ then find $r$.

Answer 1

In $\Delta AOD$

$\cos {45}^{\circ }=\frac{r}{5\sqrt{2}}$

$\frac{1}{\sqrt{2}}=\frac{r}{5\sqrt{2}}$

$r=5unit$