In a circle, AB and DC are two chords. When AB and DC are produced, they meet at P. If PC = 5.6 cm, PB = 6.3 cm and AB = 7.7 cm, then the length of CD is∶
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Correct answer: B
Explanation
The correct answer is option 2 i.e. 10.15 cm.
Given, PC = 5.6, PB = 6.3, AB = 7.7
PA = PB + AB = 6.3 + 7.7 = 14
As we know,
PC × PD = PB × PA
⇒ 5.6 × PD = 6.3 × 14
⇒ PD = (6.3 × 14)/5.6
⇒ PD = 15.75
⇒ PD = PC + CD
⇒ 15.75 = 5.6 + CD
∴ CD = 15.75 – 5.6 = 10.15 cm