From a point Q, the length of the tangent to a circle is 20 cm and the distance of Q from the centre of the circle is 25 cm. The radius of the circle is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 15 cm.
Given that
The length of the tangent to the circle (QP ) = 20 cm
The distance between point Q and center of the circle O (OQ) = 25 cm
Let the radius of a circle be r cm
According to the question
In triangle OPQ,
⇒ r2 = OQ2 - QP2
⇒ r2 = 252 - 202
⇒ r2 = 625 - 400 = 225
⇒ r = 15 cm