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In the given figure, AP = 3 cm, PB = 5 cm, AQ = 2 cm and QC = x. What is the value of x?

(a) 6 cm 

(b) 8 cm 

(c) 10 cm 

(d) 12 cm

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Answer : (c) 10 cm 

If two chords PB and QC intersect externally at a point A, then 

AB × AP = AC × AQ 

⇒ 8 × 3 = (2 + x) × 2 

⇒ 2 + x = 12 

⇒ x = 10 cm.

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