Question : In the following figure, O is the centre of the circle. Its two chords AB and CD intersect each other at point P inside the circle. If AB =18 cm, PB = 6 cm, and CP = 4 cm, then find the measure of PD.
Option 1: 14 cm
Option 2: 18 cm
Option 3: 16 cm
Option 4: 20 cm
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Correct Answer: 18 cm
Solution :
Given: Two chords AB and CD intersect each other at point P inside the circle.
AB =18 cm, PB = 6 cm and CP = 4 cm
AP = AB – PB
= 18 – 6 = 12 cm
According to the formula,
AP × PB = CP × PD
⇒ 12 × 6 = 4 × PD
⇒ PD = 3 × 6 = 18 cm
Hence, the correct answer is 18 cm.
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