Question

The length of a tangent
From a point A at distance 5cm from the
Center of the circle is 4cm. Find the radius of the circle

Answer 1

Answer:

use Pythagoras theorm

now

(R)^2= 25 - 16

(R)^2 = 9

Now Radius is 3cm answer

Answer 2

Given: Let, the circle beith centre O

AB is the tangent from point A

Length of tangent = AB = 4cm

Also, distance of point from circle=5cm

Hence, OA = 5cm

To find: Radius, i.e., OB

Solution: Since, AB is tangent

Hence, OB is perpendicular to AB

Therefore, angle of OBA = 90°

So, triangle OAB is right angle

In right angle OA

Using Pythagoras Theorem

(Hypotenuse)^2=(Height)^2+(Base)^2

(OA)^2=(OB)^2+(AB)^2

(5)^2= (OB)^2 + (4)^2

(OB)^2 = 9

(OB) = 3

Hence , radius of the circle OB = 3cm