PQ and RS are common tangents to two circles intersecting at A and B. When AB produced both sides, meet the tangents PQ and RS at X and Y respectively. If AB = 3 cm, XY = 5 cm, then PQ (in cm) will be ________.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 4 cm
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Understanding |
Application |
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PQ and RS are common tangents to two circles intersecting at A and B. AB, when produced both sides, meet the tangents PQ and RS at X and Y, respectively. AB = 3 cm, XY = 5 cm |
We know: XA = YB So, XY = XA + AB + BY ⇒ 5 = 2XA + 3 ⇒ 2XA = 5 – 3 = 2 ⇒ XA = 1 XB = XA + AB = 1 + 3 = 4 Now, PX = XA × XB ⇒ PX = 1 × 4 ⇒ PX = 2 cm Similarly, XQ = 2 cm ⇒ PQ = PX + XQ = 2 + 2 = 4 cm |
