Question

${\textbf{Subject : Mathematics}}$

${\textbf{Chapter : Tangency}}$


A point P is 16 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

Hey !

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Given : P is a point at distance of 16cm 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, 16² = OT² + (12)²

Or, 256 - 144 = OT²

Or, 112 = OT²

∴ OT = 10.59 cm

Hence, Radius = 10.59 cm

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Thanks !

Answer 2

$\huge{Given}$

A point P = 16 cm from the centre of the circle.

The lengthy of tangent drawn from P to the circle = 12 cm

Radius of circle = ?

Here

Angle OTP = 90°

In right angle triangle OTP

${op}^{2} = {ot}^{2} + {tp}^{2}$

${16}^{2} = {ot}^{2} + {12}^{2}$

$256 - 144$

$112 = {ot}^{2}$

$ot = 10.59cm$