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

Here, ∠OPO =90°

It is given that PQ =16 cm

and OQ = 12 cm

In right ΔOPQ

OQ2 = OP2 + PQ2

[Using Pythagoras theorem]

⇒ (16)2 = OP2 + (12)2

OP2 = (16)2 – (12)2

= 256– 144 = 12 ⇒ OP = 12 cm

Hence, radius of the circle = 12 cm.