Question

In the given figure, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD = 7.8 cm, PD = 5 cm, PB = 4 cm. Find:

1. AB.
2. the length of tangent PT.

Answer 1

Given that,

CD = 7.8 cm, PD = 5 cm, PB = 4 cm

As we know,

PT² = PD × PC

PT² = PD × (PD + CD)

PT² = 5 × 12.8

PT² = 64

`=>` PT = 8 cm

Now in ΔPOT,

PO² = OT² + PT²

(r + 4)² = r² + 64

r² + 16 + 8r = r² + 64

8r = 48

r = 6

1. Thus AB = 2r = 12 cm
2. Length of tangent PT = 8 cm.