question_answer

If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is \[60{}^\circ \], then find the length of OP.

Answer:

Given,   \[\angle APB=60{}^\circ \]

\[\Rightarrow \] \[\angle APO=30{}^\circ \]

In right angle\[\Delta \text{ O}AP\],

\[\frac{OP}{OA}=\cos ec\,\,30{}^\circ \]

\[\frac{OP}{a}=2\Rightarrow OP=2a\]