Question

Length of a tangent segment drawn from a point which is at a distance 15 cm
from the centre of a circle is 12 cm, find the diameter of the circle?​

Answer 1

Let external point be B. OA be radius of circle.

Given:

OB=12.5 cm

AB=12 cm

In right triangle, AOB, by Pythagoras Theorem,

OB

2

=AB

2

+OA

2

AO

2

=OB

2

−OA

2

=12.5

2

−12

2

=12.25

∴AO=3.5 cm

Diameter=2(AO)=2(3.5)=7 cm