Question

if the angle between two tangents draw from an external point P to a circle of radius and a centre O, is 60degree,then find the lenght of OP

Answer 1

What is the radius for above question

Answer 2

Answer: OP=2a

Step-by-step explanation: let "a" be the radius.

Now, the angle between two tangents is 60, which means that when we join OP, angle 60 is bisected.

This, angle APB is bisected as: APO+BPO

30°+30°

Now, you know that In triangle OAP angle A= 90

Hence by trigonometric ratios-

Sin30°= OA/OP

1/2= a/OP

Thus, OP=2a