Question

the length of a tangent from a point a at a distance 5 cm from the centre of the circle is 4 cm find the radius of the circle

Answer 1

The centre of the circle is O AP = 4cm and OA= 5cm To find: OP In a right angled triangle, by Pythagoras theorem OP= $\sqrt{OA ^{2} - AP ^{2} }$ OP= $\sqrt{5 ^{2}- 4 ^{2} }$ OP= 3 cm

Answer 2

Given :

• Length of OA = 5 cm

• Lenght of AB = 4 cm

To Find :

• Length of OB ( radius )

Solution :

As we know ABO is a right angled triangle. So we can use Pythagoras theorem to find radius.

( OA )² = ( AB )² + ( OB )²

Substitute values in formula

⇒ 5² = 4² + ( OB )²

⇒ 25 = 16 + ( OB )²

⇒ ( OB )² = 25 - 16

⇒ ( OB )² = 9

⇒ OB = √9

⇒ OB = 3

Radius of circle is 3 cm