Two tangents are drawn from a point P outside a circle of radius 5 cm. The angle between the tangents is 90°, and the distance from P to the center of the circle is R cm. Find the value of R.
Show answer & explanation
Correct answer: C
Explanation
Given:
Radius of the circle = 5 cm
Angle between the tangents = 90°
Distance of point P from the center = R
By the formula:
Center OP bisects the angle
Hence ∠OPT = 45°
At the point of contact
OT ⟂ PT
In triangle OPT
sin45° = OT / OP
1/√2 = 5 / R
R = 5 × 1.414
R = 7.07 cm