Question

The length of a tangent from a point Aat distance 5cm from the centre of the circle is 4cm.Find
the radius of the circle.

​

Answer 1

$x=3cm {}^{}$

Answer 2

Answer:

Let AT be the tangent drawn from a point A to a circle with center  

O and OA=5 cm and AT=4 cm. Since tangent at a point is  

perpendicular to the radius through the point of contact

∴OT⊥AT

∴ from right-angled △OAT,

   ( OA )² = ( OT )² + ( TA )²

   ( 5 )² = ( OT )² + ( 4 )²

   ( OT )² = 25 - 16

   ( OT )² = 9

     OT = ²√9

     OT = 3

∴ Radius of the circle =3 cm.