Question

In the given figure ,two tangents $PA$ and $PB$ are drawn to the circle with centre $O$,such that $\angle APO={60}^o$.Prove that $OP=2AP$

Answer 1

since OA is the radius of given circle

and PA is the tangent to the given circle

we know that tangent and radius is perpendicular at the point of contact

$so,PA\perp OAand\angle APO={60}^{o}In\Delta APO\cos \theta =\frac{b}{h}\Rightarrow \cos {60}^o=\frac{AP}{OP}\Rightarrow \frac{1}{2}=\frac{AP}{OP}\Rightarrow OP=2AP$