Question

Find the area of the circle if 8 cm is the length of the tangent, 11 cm is the distance between the center of the circle the external point.

(a) 100 cm

(b) 110 cm

(c) 197.14 cm

(d) 179.14 cm

The question was posed to me in class test.

My doubt stems from Tangent to a Circle in chapter Circles of Mathematics – Class 10

Answer 1

Correct choice is (d) 179.14 cm

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 = √57

Area of the circle = πr^2

= \(\frac {22}{7}\)(√57)^2

= 179.14