Question

1. A point P is at a distance of 29 cm from the centre of a circle of radius 20 cm. Find the length of the tangent drawn from P to the circle.​

Answer 1

Given Information :-

OT = Radius = 20 cm

OP = 29 cm

Need to find :-

Find the length of the tangent drawn from P to the circle ?

Solution :-

OT is radius of a circle and PT is the tangent of a circle.

OT ⊥ PT

• By using Pythagoras theorem :

(OP)² = (PT)² + (OT)2

(29)² = (PT)² + (20)²

841 = (PT)² + 400

(PT)² = 841 - 400

(PT)² = 441

PT = √441

PT = 21

Hence,

• The length of the tangent drawn from P to the circle is 21 cm.

Answer 2

Given :-

A point P is at a distance of 29 cm from the centre of a circle of radius 20 cm

To Find :-

The length of the tangent drawn from P to the circle

Solution :-

At first see the attachment ;

You will find that :-

• O is centre of Circle with Radius 20 cm
• OP = 29 cm
• Angle made by Point of Contact = 90°
• Radius of Circle with centre O = 20 cm = OA

Let , us assume that ;

• The point where The tangent touches the circle = A
• OA = x cm

In right angled ∆OAP ;

By Pythagoras Theorem ;

${ \quad \qquad \leadsto \sf OP² = OA² + AP² }$

${ : \implies \quad { \sf ( 29 )² = ( 20 )² + x² }}$

${ : \implies \quad { \sf x² + 400 = 841 }}$

${ : \implies \quad { \sf x² = 841 - 400 }}$

${ : \implies \quad { \sf x² = 441 } }$

${ : \implies \quad { \sf x = \sqrt{441}}}$

${ : \implies \quad { \sf x = 21 \:\: cm }}$

$\quad \qquad { \bigstar { \underline { \boxed { \red { \bf \therefore AP = 21 \:\: cm }}}}}{\bigstar}$

Henceforth , The Required Answer Is 21 cm