Question

a point b is 17cm away from the centre o of a circle. ab is the tangent to the circle at a. given that ab = 15 cm, find the radius of the circle. 2 cm 8 cm 9 cm 16 cm

Explanation:

Step1: Recall tangent-radius property

A tangent to a circle is perpendicular to the radius at the point of contact. So, \( \angle OAB = 90^\circ \), making \( \triangle OAB \) a right triangle with \( OB = 17 \, \text{cm} \), \( AB = 15 \, \text{cm} \), and \( OA \) (radius, \( r \)) as one leg.

Step2: Apply Pythagorean theorem

In right triangle \( OAB \), \( OA^2 + AB^2 = OB^2 \). Let \( OA = r \). Then \( r^2 + 15^2 = 17^2 \).

Step3: Solve for \( r \)

Calculate \( 17^2 = 289 \) and \( 15^2 = 225 \). So, \( r^2 = 289 - 225 = 64 \). Take the square root: \( r = \sqrt{64} = 8 \, \text{cm} \).

Answer:

8 cm