Question

Q.10- The length of a tangent from a point A at distance 5 cm from the centre of the
circle is 4 cm. Find the radius of the circle.
​

Answer 1

Given

AC=5

AB4

We want r=?

Tangent makes an angle 90

o

with centre

∴ABC is right triangle

AC

2

=BC

2

+AB

2

5

2

=r

2

+4

2

⇒r

2

=25−16=9

⇒r=3.

Answer 2

Step-by-step explanation:

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

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

⇒25−16=(OT) 2

⇒9=(OT) 2

⇒OT=3 cm

∴ radius of the circle =3 cm.