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

Answer:

we have to find the length of tangent drawn from a point 13cm away from the centre of a circle of radius 12cm.

Let tangent is drawn from P which touches the circle at T. e.g., length of tangent is PT and centre of circle is O.

Given, PO = 13cm , OT = radius = 12cm

we know, tangent is perpendicular upon radius of circle so, ∆POT is right angled triangle.

so, PT² + OT² = OP²

PT² + 12² = 13²

PT² = 169 - 144 = 25

PT = 5cm

hence, length of tangent = 5cm