Question : In the figure, O is the centre of the circle. Its two chords AB and CD intersect each other at the point P within the circle. If AB = 20 cm, PB = 12 cm, and CP = 8 cm, then find the measure of PD.
Option 1: 12 cm
Option 2: 11 cm
Option 3: 22 cm
Option 4: 14 cm
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Correct Answer: 12 cm
Solution : Given that two chords AB and CD intersect each other at point P. AB = 20 cm, PB = 12 cm, and CP = 8 cm If two chords AB and CD intersect each other at point P inside the circle, then AP $×$ PB = CP $×$ PD ⇒ (20 - 12) $×$ 12 = 8 $×$ PD ⇒ 8$×$ 12 = 8 $×$ PD ⇒ PD = 12 cm Hence, the correct answer is 12 cm.
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