Question : The chords PQ and RS of a circle, when produced, meet at a point O. If PQ = 6 cm, OQ = 8 cm, and OS = 7 cm, then the length (in cm) of the chord RS is:
Option 1: 10
Option 2: 12
Option 3: 16
Option 4: 9
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Correct Answer: 9
Solution :
We know that the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.
⇒ OP × OQ = OR × OS
Given that PQ = 6 cm, OQ = 8 cm, and OS = 7 cm.
On substituting the values,
⇒ (6 + 8) × 8 = OR × 7
⇒ 2 × 8 = OR
⇒ OR = 16 cm
⇒ RS = OR – OS = 16 – 7 = 9 cm
Hence, the correct answer is 9.
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