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Problems from Another Time

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

The perimeters of two similar triangles are 45 and 135 respectively. One side of the first triangle has length 11″ and a second side, 19″. Find the lengths of the sides of the second triangle.
Given two circles tangent to each other and to a common line, determine a relationship between the radii and the distance between the tangent points.
What is the value of X...
A set of four congruent circles whose centers form a square is inscribed in a right triangle ABC where C is the right angle and serves as one corner of the square. Find their radius in terms of the sides; a,b,c, of the triangle.
On a day in spring a boy has gathered cherry blossoms under a cherry tree. Nearby a poet is reading some of his poems aloud. As he reads, the boy counts out the cherry blossoms, one blossom for each word of a poem.
Two ants are 100 paces apart, crawling back and forth along the same path. The first goes 1/3 pace forward a day and returns 1/4 pace; the other goes forward 1/5 pace and returns 1/6 pace. How many days before the first ant overtakes the second?
Given four integers where if added together three at a time their sums are: 20, 22, 24, and 27. What are the integers?
Suppose a man had put out one cent at compound interest in 1620, what would have been the amount in 1824, allowing it to double once in 12 years?
In the figure at the left, if the radii of each inscribed circle is 1, what are the dimensions of the bounding rectangle?
A circle, a square and an equilateral triangle all have the same perimeter equal to 1 meter. Compare their areas.

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