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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:
- AB.
- the length of tangent PT.
Solution
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
- Thus AB = 2r = 12 cm
- Length of tangent PT = 8 cm.
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