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Photo: DER SPIEGEL
This week's puzzle is comparatively easy, as long as you are not at war with geometry.
A circular ring is given.
We do not know its dimensions.
But we know that a ten centimeter long rod fits exactly on the circular ring.
In such a way that it touches the inner edge of the ring - and that the two ends of the rod touch the outer edge without protruding beyond the ring - see sketch above.
So that we can calculate better, we assume that the rod has a diameter of zero.
How big is the area of the annulus?
The area is Pi * 25 cm2.
The area of the annulus is calculated using the formula Pi * (R2 - r2).
The radii R, r and half the rod length 5 form a right-angled triangle - see the following sketch.
The Pythagorean theorem solves the problem of the two unknowns r and R. The following applies:
52 + r2 = R2
And thus:
R2 - r2 = 25
Accordingly, Pi * (R2 - r2) = Pi * 25.
If you missed a puzzle from the past few weeks, here are the most recent episodes:
Buying a bicycle with counterfeit money
Six acute angles
How far is it to the neighboring village?
How old is sophie
Triangle searched on three circles
Pirates fight over 120 gold coins
December 31st wins
What time is it?
Pretty weird
The perfect egg
