In the adjoining figure, $P A$ and $P B$ are tangents to a circle with centre $O$ such that $\angle

Question

In the adjoining figure, $P A$ and $P B$ are tangents to a circle with centre $O$ such that $\angle P=90^{\circ}$. If $A B=3 \sqrt{2} \mathrm{~cm}$, then the diameter of the circle is\

Professor PC Thomas Classes · Answer

(d): Given, $\angle P=90^{\circ}, A B=3 \sqrt{2} \mathrm{~cm}$.\ $P A$ and $P B$ are tangents.\ So, $\angle O B P=\angle O A P=90^{\circ}$ and $\angle P=90^{\circ} \Rightarrow \angle O=90^{\circ}$.\ $\Rightarrow O A P B$ is a square.\ Since, $A B=O A \sqrt{2}$\ $\Rightarrow \quad 3 \sqrt{2}=O A \sqrt{2} \Rightarrow O A=3$\ ⇒ Diameter $=2, O A=2 	imes 3=6 \mathrm{~cm}$