Question

Find the length of the tangent drawn from a point whose distance from the center of a circle is 25 cm. Given that the radius of the circle is 7 cm. [3 MARKS]

Answer 1

Concept: 1 Mark
Application: 2 Marks

Let P be the given point , O be the center of the circle and PT be the lenght of tangent from P .

Then, OP= 25 cm and OT = 7 cm

Since tangent to a circle is always perpendicular to the radius through the points of contact.

Therefore , $\angle OTP={90}^{\circ }$

In right triangle OTP , We have

$\Rightarrow O{P}^2=O{T}^2+P{T}^2$

$\Rightarrow {25}^2=7^2+P{T}^2$

$\Rightarrow P{T}^2={25}^2-7^2=(25-7)(25+7)=576$

$\Rightarrow PT=24$

Hence, length of tangent from P = 24 cm