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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