Problem 12 · 2016 Math Kangaroo
Stretch
Geometry & Measurement
pythagorean-triple
A 3×3 field is made up of 9 unit squares. In two of these squares, circles are inscribed as shown in the diagram. How big is the shortest distance between these circles?
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Answer: A — 2√2 − 1
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Hint 1 of 2
The two circles sit in opposite corner squares; find the distance between their centres first.
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Hint 2 of 2
Subtract one radius from each circle from the centre-to-centre distance.
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Approach: distance of centres minus radii
- Each circle has radius 1/2 and its centre at the middle of a corner unit square.
- The centres are 2 right and 2 up apart, a distance of 2√2.
- Removing the two radii gives the gap 2√2 − 1, so 2√2 − 1.
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