If two tangents inclined at an angle 60° are drawn to a circle of radius 5 cm, then what is the length of each tangent?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(5\sqrt{3}\) cm
Two facts about tangents from an outside point P decide this: the radius to the point of contact is perpendicular to the tangent, and the line PO to the centre bisects the angle between the two tangents. So the 60° angle splits into two angles of 30°.
In triangle OAP, the angle at A is 90° and the angle at P is 30°
\(\displaystyle \tan30^\circ=\frac{OA}{PA}\), so \(\displaystyle \frac{1}{\sqrt{3}}=\frac{5}{L}\)
\(L=5\sqrt{3}\) cm, the length of each tangent (the two tangents from P are equal)