Question

A tangent is drawn from an external point P to a circle of 8 cm radius. If the length of the tangent is 15 cm then the distance between the centre of the circle and point P is

• A. 23 cm
• B. 20 cm
• C. 17 cm
• D. Cannot be determined

Answer 1

The Correct Option is C

In this problem, we are given a circle with a radius of 8 cm, and a tangent drawn from an external point \( P \) to the circle with a length of 15 cm. The distance between the center of the circle and the external point \( P \) can be found using the Pythagorean theorem. The radius of the circle, the length of the tangent, and the distance between the center of the circle and the external point form a right triangle, where: 
One leg is the radius (\( r = 8 \) cm),
The other leg is the length of the tangent (\( t = 15 \) cm),
The hypotenuse is the distance from the center of the circle to the external point \( P \). According to the Pythagorean theorem: \[ \text{Distance}^2 = r^2 + t^2 \] Substituting the known values: \[ \text{Distance}^2 = 8^2 + 15^2 = 64 + 225 = 289 \] \[ \text{Distance} = \sqrt{289} = 17 \, \text{cm} \]

The correct option is (C): \(17\ cm\)