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

Since tangent to a circle is perpendicular to the radius throgh the point of contact.

⇒ ∠OTP = 90°

In right ΔOTP, we have

OP2 = OT2 + PT2

⇒ (13)2 = OT2 + (12)2

OT2 = 169 – 144 = 25

⇒ OT = 5

Hence, the radius of the circle is 5 cm.