Question

in the figure O is the centre of the circle PT is the tangent and plm is a secant passing through Centre O if PT is equal to 8 cm and PR is equal to 4 cm then find the radius of the circle ​

Answer 1

Answer:

Step-by-step explanation:

Let radius = x

In triangle OTP

(X+4)^2 = x^2 + 8^2 ( since pythagoras theorem)

X^2 + 8x + 16 = x^2 + 64

8x= 64-16

X=48/8

X = 6cm = radius of circle

Answer 2

Given,

In the figure, O is the centre of the circle PT is the tangent and PLM is a secant passing through Centre O. PT is equal to 8 cm and PR is equal to 4 cm

To find,

The radius of the circle.

Solution,

Let radius of the circle be x.

We know that,

PT = 8cm

PR = 4cm

PT is a tangent to the circle.

So, OT will be perpendicular to PT.

⇒ ∠OTP = 90°

Using Pythagoras Theorem, In triangle OTP,

$(x+4)^2 = x^2 + 8^2$

$x^2 + 8x + 16 = x^2 + 64$

8x = 64 - 16

8x = 48

x = 48/8

x  = 6cm

Hence, radius of the circle is 6cm.