If a tangent to a circle from a point P meets the circle at A with AP =15cm. Given that the radius of the circle is 8 cm, find the distance of P from the centre of the circle.

Correct option is B

Given:

Length of the tangent: AP = 15cm

Radius of the circle: r = 8 cm

Concept Used:
A tangent to a circle is perpendicular to the radius at the point of tangency. 

Solution: 

where:

OP is the distance of P from the center of the circle.

From the property of the tangent;

OP² = AP² + r² ( Pythagorean theorem)​

OP² = 15² + 8²​

OP² = 225 + 64

OP = 17cm

Thus distance of P from the center of the circle is ​17 cm.