Question

Find the radius of a circle if 8 m is the length of the tangent, 11 m is the distance between the center of the circle the external point.

(a) 7 m

(b) 5 m

(c) √57 m

(d) √58 m

I have been asked this question in class test.

Asked question is from Tangent to a Circle in portion Circles of Mathematics – Class 10

Answer 1

The correct option is (c) √57 m

Explanation: Length of the tangent = \(\sqrt {d^2-r^2}\)

8 = \(\sqrt {11^2-r^2}\)

r^2 =  11^2 – 8^2

r = \(\sqrt {11^2-8^2}\)

r = \(\sqrt {121-64}\)

r = √57