Question

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 ______.

Options

• 7 cm

• 12 cm

• 15 cm

• 24.5 cm

Answer 1

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 7.

Explanation:

 

Let O be the centre of the circle.

Given that,

OQ = 25cm and PQ = 24 cm

As the radius is perpendicular to the tangent at the point of contact,

Therefore, OP ⊥ PQ

Applying Pythagoras theorem in ΔOPQ, we obtain,

OP² + PQ² = OQ²

OP² + 24² = 25²

OP² = 625 − 576

OP² = 49

OP = 7

Therefore, the radius of the circle is 7 cm.

Hence, alternative 7 cm is correct.