Problem 9 · 2018 Math Kangaroo
Easy
Geometry & Measurement
spatial-reasoning
Two circles are inscribed in an 11 cm long and 7 cm wide rectangle so that they each touch three sides of the rectangle. How big is the distance between the centres of the two circles?
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Answer: D — 4 cm
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Hint 1 of 2
Each circle touches three sides, so its size is fixed by the short side of the rectangle.
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Hint 2 of 2
Find each centre's distance from the left and right ends; subtract.
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Approach: locate the two centres and subtract
- Touching three sides means each circle has diameter 7 cm (the width), so radius 3.5 cm.
- The left centre sits 3.5 cm from the left edge; the right centre sits 3.5 cm from the right edge of the 11 cm length.
- Distance between centres = 11 − 3.5 − 3.5 = 4 cm.
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