Question : Two chords AB and CD of a circle meet inside the circle at point P. If AP = 12 cm, AB = 20 cm, and CP = 16 cm, find CD.
Option 1: 22 cm
Option 2: 15 cm
Option 3: 21 cm
Option 4: 24 cm
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Correct Answer: 22 cm
Solution :
Given: AB = 20 cm, AP = 12 cm, and CP = 16 cm
Also, AB = AP + PB
⇒ 20 cm = 12 cm + PB
⇒ PB = 8 cm
We know, AP × PB = CP × PD
By substituting the values in the above expression,
12 × 8 = 16 × PD
⇒ PD = 6 cm
Then, CD = CP + PD = 16 + 6 = 22 cm
Hence, the correct answer is 22 cm.
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