Question

If the angle between two tangents drawn from an external point P to the circle of radius a and center O is:

(a) 90∘, then OP=2a.

(b) 60∘, then OP=a.

(c) 120∘, then OP=3a.

(d) 180∘, then OP=[infinity].

Answer 1

The angle between tangents and the radius of a circle determines the length of OP.

Step-by-step explanation:

The angle between two tangents drawn from an external point P to a circle of radius a and center O depends on the position of P with respect to the circle.

If the angle is 90∘, then OP=2a.

If the angle is 60∘, then OP=a.

If the angle is 120∘, then OP=3a.

If the angle is 180∘, then OP=[infinity].