Question

Q. 7 The length of a tangent drawn from a point 13 cm away from the centre of a circle of radius 5 cm is -
(a) 12 cm
(b) 2 V7 cm (c) 16 cm
(d) 10 cm​

Answer 1

Answer:

option b is right

I think

Answer 2

$\LARGE\underline{\underline{\sf Given:}}$

• Point= 13cm

• Radius of circle (R) = 5cm

$\LARGE\underline{\underline{\sf To\:Find:}}$

• Length of tangent = ?

$\LARGE\underline{\underline{\sf Solution:}}$

Let ,

Tangent is drawn from P and it touches circle at T

•°•

Length of tangent = PT

And

Centre of Circle = O

OP= 13cm (Given)

Radius (OT) = 5cm

We know ,

Tangent is perpendicular upon radius of circle

So ,

∆POT is right angle triangle

$\large\implies{\sf PT^2+OT^2= OP^2}$

$\large\implies{\sf PT^2+5^2=13^2 }$

$\large\implies{\sf PT^2=169-25 }$

$\large\implies{\sf PT^2=144cm}$

$\large\implies{\sf PT=\sqrt{144}}$

$\large\implies{\sf PT=12\:cm }$

$\LARGE\underline{\underline{\sf Answer:}}$

Option (a) 12cm

•°• Length of tangent is 12cm