Question

From an external point Q, the length of tangent to a circle is 12 cm and the diatance of Q from the centre of circle is 13 cm. The radius of circle (in cm ) is

A. 10
B. 7
C. 5
D. 12

Answer 1

Using the Pythagorean theorem on the right-angled triangle formed by the radius, tangent, and distance from the external point to the center of the circle, we find that the radius of the circle is 5 cm.

Step-by-step explanation:

To find the radius of the circle, we can use the Pythagorean theorem. We are given that the length of the tangent from point Q to the circle is 12 cm, and the distance from point Q to the center of the circle is 13 cm. Since the tangent is perpendicular to the radius of the circle at the point of contact, we have a right-angled triangle formed by the radius (r), the length of the tangent (12 cm), and the distance from Q to the center (13 cm).

Using the Pythagorean theorem:

r^2 + 12^2 = 13^2

r^2 + 144 = 169

r^2 = 169 - 144

r^2 = 25

r = 5 cm

Therefore, the radius of the circle is 5 cm, making the correct answer (C) 5 cm.