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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.
Solution
PA = AB + BP = (AB + 4) cm
PC = PD + CD = 5 + 7.8 = 12.8 cm
Since PA × PB = PC × PD
⇒ (AB + 4) × 4 = 12.8 × 5
⇒ AB + 4 =
⇒ AB + 4 = 16
⇒ AB = 12 cm
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