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Problems from Another Time

Individual problems from throughout mathematics history, as well as articles that include problem sets for students.

A circle is inscribed in an isosceles trapezoid. Find the relationship of the radius to the sides.
A cat sitting on a wall 4 cubits high saw a rat prowling 8 cubits from the foot of the wall.
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
Now a pile of rice is against a wall with a base circumference 60 chi and an altitude of 12 chi.
Now a good horse and an inferior horse set out from Chang'an to Qi. Qi is 3000 li from Chang'an.
Given a guest on horseback rides 300 li in a day. The guest leaves his clothes behind. The host discovers them after 1/3 day, and he starts out with the clothes.
Three circles of varying radius are mutually tangent. The area of the triangle connecting their centers is given. Find the radius of the third circle.
A certain slave fled from Milan to Naples going 1/10 of the whole journey each day. At the beginning of the third day, his master sent a slave after him and this slave went 1/7 of the whole journey each day.
Given two circles tangent at the point P with parallel diameters AB and CD, prove that APD and BPC are straight lines.
Suppose the area of an equilateral triangle be 600. The sides are required.