Question:
If angle between two tangents drawn from a point P to a circle of radius a and centre 0 is 90°, then OP = a √2.
Solution:
True
From point $P$, two tangents are drawn.
Given, $O T=a$
Also, line OP bisects the $\angle R P T$.
$\therefore$ $\angle T P O=\angle R P O=45^{\circ}$
Also, $O T \perp P T$
In right angied $\triangle O T P$. $\sin 45^{\circ}=\frac{O T}{O P}$
$\Rightarrow$ $\frac{1}{\sqrt{2}}=\frac{a}{O P} \Rightarrow O P=a \sqrt{2}$