Sunday Times Teaser 2514 – No Title
by Des MacHale
Published November 28 2010 (link)
The Hardy Annular is an ornamental garden consisting of the area between two circles with the same centre, with the radius of each a whole number of metres. A line joining two points on the circumference of the bigger circle just touches the smaller circle and measures exactly 20 metres.
What is the radius of each of the circles?
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Brian Gladman permalink1234567891011# For large (R) and small (r) and chord half length (x):## (x / 2)^2 = (R - r).(R + r) with x = 20# consider possible values for R - r, R + r = 100 / (R - r)for n in range(1, 10):r = (100 / n - n) / 2if int(r) == r:print(f'Radii {r:.0f} and {r + n:.0f} metres.')
