Question

${\textbf{Subject : Mathematics}}$

${\textbf{Chapter : Tangency}}$


A point P is 13 cm from the centre of the circle. The length of tangent drawn from P to the circle is 12 cm. Find the radius of the circle.​

Answer 1

Given : P is a point at distance of 13cm from the centre of a circle O. The length of tangent drawn from P to the circle is 12 cm.

It is required to measure the radius of the circle.

Now, ∠OTP= 90°

( ∵ a tangent to a circle is ⊥ to the radius through the point of contact).

∴ In right angle triangle OTP,

OP² = OT²+ TP²

Or, 13² = OT² + (12)²

Or, 169-144 = OT²

Or, 25 = OT²

∴ OT = 5 cm

Hence, Radius = 5 cm

Answer 2

Point P is 13 cm away from the centre...

Here's the reason why..

Since tangent to a circle are perpendicular to the radius through the point of contact....therefore in ΔOAB

∠OAB=90°

Now on applying Pythagoras theoram

$AB {}^{2} = OB {}^{2} + OA {}^{2} \\ </p><p>Therefore \: AB {}^{2} = 12 {}^{2} + 5 {}^{2} \\ </p><p>Ab {}^{2} = 144 + 25 \\ </p><p>AB {}^{2} = 169 \\ </p><p>Ab {}^{2} = 13 {}^{2}$

$Hence \: AB=13 cm$