Question

A point P is 10 cm from the center of a circle. The length of the tangent drawn from P to the circle is 8 cm. The radius of the circle is equal to ______ 

Options

• 4 cm

• 5 cm

• None of these

• 6 cm

Answer 1

A point P is 10 cm from the center of a circle. The length of the tangent drawn from P to the circle is 8 cm. The radius of the circle is equal to 6 cm.

Explanation:

Given that OP = 10 cm, PQ = 8 cm

As a tangent to a circle is perpendicular to the line joining the centre of the circle to the tangent at the point of contact to the circle.

Angle OQP = 90²

Applying Pythagoras theorem to triangle OPQ

OQ² + QP² = OP²

OQ² + 8² = 10²

OQ² = 100 - 64

= 36

OQ = 6 cm.

The radius of the circle is 6 cm.