Question

Question 5
If angle between two tangents drawn from a point P to a circle of radius a and centre 0 is ${90}^{\circ }$, then OP = a $\sqrt{2}$.

Answer 1

True

From point P, two tangents PT and PR are drawn.
Given: OT = a
Also, line OP bisects the $\angle$ RPT
$\therefore \angle TPO=\angle RPO={45}^{\circ }AlsoOT\perp PTInrightangled\Delta OTP,sin{45}^{\circ }=\frac{OT}{OP}\Rightarrow \frac{1}{\sqrt{2}}=\frac{a}{OP}\Rightarrow OP=a\sqrt{2}$