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Three circles touch one another externally. The distances between their centres are 7 cm, 8 cm and 9 cm. What is the radius of the largest circle?

Competition practiceGeometry
  • A5 cm
  • B4 cm
  • C4.5 cm
  • D6 cm

Step-by-Step Solution

With radii a, b, c: a + b = 7, b + c = 8, a + c = 9. Adding, a + b + c = 12, so the radii are 12 − 8 = 4, 12 − 9 = 3 and 12 − 7 = 5 cm. The largest is 5 cm.
Answer: A) 5 cm

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