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If the shortest distance of a given point to a given circle is \(4 \, \text{cm}\) and the longest distance is \(9 \, \text{cm}\), then the radius of the circle is

Question and options

If the shortest distance of a given point to a given circle is 4 cm4 \, \text{cm} and the longest distance is 9 cm9 \, \text{cm}, then the radius of the circle is
  1. 1.5 cm1.5 \, \text{cm} or 13 cm13 \, \text{cm}
  2. 2.5 cm2.5 \, \text{cm}
  3. 3.5 cm3.5 \, \text{cm}
  4. 2.5 cm2.5 \, \text{cm} or 6.5 cm6.5 \, \text{cm}

Answer and explanation

Correct answer: D - \(2.5 \, \text{cm}\) or \(6.5 \, \text{cm}\)
If the point is inside, diameter = 4+9 = 13 so r = 6.5; if outside, diameter = 9-4 = 5 so r = 2.5. Both cases possible.

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  • IPMAT Indore

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