Question

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

Step-by-step explanation:

In triangle POA, by pythagoras theorem

OP^2+AO^2=AP^2

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

OP^2=25-16

OP=+-√9

OP=3.

HENCE RADIUS OF THE CIRCLE IS 3cm.

Answer 2

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Draw the diagram as shown below.

Ncert solutions class 10 chapter 10-8

Here, AB is the tangent that is drawn on the circle from a point A.

So, the radius OB will be perpendicular to AB i.e. OB ⊥ AB

We know, OA = 5cm and AB = 4 cm

Now, In △ABO,

OA2 =AB2+BO2 (Using Pythagoras theorem)

52 = 42+BO2

BO2 = 25-16

BO2 = 9

BO = 3

So, the radius of the given circle i.e. BO is 3 cm.