Question

4. In the fig., O is the centre of the circle, PT is the
tangent and PLM is the secant passing through
centre O. If PT = 8 cm and PL = 4 cm, then find the
radius of the circle.
T
8 cm
M
Р
0
L
4 cm​

Answer 1

Answer:

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}(3+r)

2

=6

2

+r

2

⇔ 9 + r^{2} +6r = 36 + r^{2}9+r

2

+6r=36+r

2

⇔ 6r = 276r=27

⇒ r = \frac{9}{2} = 4.5 cmr=

2

9

=4.5cm

Hence, our radius is equal to 4.5 cm