Question

O is the centre of circle ,PT is the tangent drawn from the point P to the circle and PAB passes through the centre O of the circle . If PT = 6cm and PA = 3cm ,then find the radius of the circle

Answer 1

Answer:

The radius is equal to 4.5 cm.

Step-by-step explanation:

Since O is the center of circle ,PT is the tangent drawn from the point P to the circle and PAB passes through the center O of the circle . If PT = 6 cm and PA = 3 cm ,then our aim is to find the radius of the circle

In the picture bellow we can see O as the center of the circle, and the tangent which begins from the point P to PAB and passes through the center O of the circle is PT.

Let r be the radius of the circle.

We have that PT = 6 cm and PA = 3 cm, then by Pythagoras's theorem:

$(3+r)^{2} = 6^{2} +r^{2}$

⇔ $9 + r^{2} +6r = 36 + r^{2}$

⇔ $6r = 27$

⇒ $r = \frac{9}{2} = 4.5 cm$

Hence, our radius is equal to 4.5 cm.

Answer 2

Answer:

let r be the radius of the circle

we have that PT =6cm and PA =3 cm then by Pythagoras theorems

=(3+π) square=6 square +r square

=9 + r +6r =36 +r square

=6r =27

=r =9/2=4.5

Step-by-step explanation:

your answer is 4.5