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Question

In the figure given below, 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.  Select the statements that are true.



Your Answer
A

AB = 9 cm

Correct Answer
B

AB = 12 cm

Your Answer
C

PT = 2 cm

Your Answer
D

PT = 8 cm


Solution

The correct option is B

AB = 12 cm


PT is tangent and PDC is secant out to the circle
PT2=PC×PD
PT2=(5+7.8)×5=12.8×5
PT2=64PT=8 cm
In ΔOTP
PT2+OT2=OP2
82+x2=(x+4)264+x2=x2+16+8x
6416=8x48=8x
x=488=6 cm
Radius=6 cm
AB=2×6=12 cm

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