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Convergence articles

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There are a number of wonderful mathematics websites that readers of Convergence should be aware of. We describe some of them here.
Given a semicircle, Prove that if O is the circle's center, DO=OE.
A man bought a number of sheep for $225; 10 of them having died, he sold 4/5 of the remainder for the same cost and received $150 for them. How many did he buy?
The radius of a circle is 3.20 meters. Compute to within .001m the areas of the inscribed and circumscribed equilateral triangles.
Two travelers, starting at the same time from the same point, travel in opposite directions round a circular railway.
What is the value of X...
A method for extracting square roots used in Italy through the 18th century was introduced in a manuscript by the 12th century mathematician al-Hassar. Appendix: When Was Fermat Born? (Not in 1601 ...)
It is required to determine whether 30 horses can be put into 7 stalls; so that in every stall there may be, either a single horse, or an odd number of horses.
Given the cats eye as shown. Let the radius of the eye be given by R. What is the area of the pupil?
A translation from the original Greek of a manuscript on magic squares by the Byzantine scholar Manuel Moschopoulos, written about 1315