Question

length of a tangent segment from point at a distance 15cm from the centre is 12 cm. find the diameter of circle

Answer 1

Given

We have given length of tangent = 15cm

length of tangent segment from its centre is 12cm

To Find

We have to find diameter of the circle

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Construction

Draw an external point B just outside the Circle.

Now,OA be the radius of the circle

In ∆AOB

↣OB= 15cm[given]

↣AB=12 cm[given]

Now,In ∆AOB

By applying Pythagoras theorem

↣OB²=OA²+AB²

↣15²=OA²+12²

↣225=OA²+144

↣225-144=OA²

↣OA²=81

↣OA=√81=9

↣OA=9cm

Therefore,OA= 9cm

Diameter of the circle = 2(OA)=2(9)=18cm