In the given figure, the diameter AB and chord CD of a circle meet at P. PT is tangent to the circle at T. If CD = 8 cm, PD = 10 cm, and PB = 8 cm, find AB.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 14.5 cm.
Given that
If CD = 8 cm, PD = 10 cm and PB = 8 cm
PT is a tangent to the circle at T
Concept
According to the tangent theorem,
PC × PD = PT2 = AP × BP
Calculation
⇒ PC = PD + CD = 10 + 8 = 18 cm
⇒ PC × PD = AP × BP
⇒ 18 × 10 = AP × 8
⇒ AP = 22.5 cm
⇒ AB + BP = 22.5
Hence, AB = 22.5 - 8 = 14.5 cm