# From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the Centre is 25 cm. The radius of the circle is.

Important NCERT Questions

Circles

NCERT Books for Session 2022-2023

CBSE Board and UP Board Others state Board

EXERCISE 10.2

Page No:213

Questions No:1

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Let O be the centre of the circle.

Given: OQ = 25 cm and PQ = 24 CM

We Know that the radius is perpendicular to tangent. Therefore, OP ⊥PQ

In ΔOPQ, by pythagoras theorem,

OP² + 24² = 25² ⇒ OP² = 625 – 576 ⇒ OP² = 49 ⇒OP = 7

Therefore, the radius of circle is 7 cm. Hence, the option (A) is correct.