Monthly Archives: July 2012

Three Circles Inscribed in a Rectangle

Three congruent circles with centers and are tangent to the sides of rectangle as shown. The circle centered at has diameter and passes through points and . Find the area of the rectangle. Source: Julia Robinson Mathematics Festival SOLUTION Radius … Continue reading

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Three Large Squares

Each of the three large squares shown below is the same size. Segments that intersect the sides of the squares intersect at the midpoints of the sides. How do the shaded areas of these squares compare? Source: Julia Robinson Mathematics … Continue reading

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Water Bucket Conundrum

You are staying at a rural cabin and the only method to get water is to draw it from a well. A 4-gallon bucket and a 9-gallon bucket are the only containers for carrying water to the cabin. In one … Continue reading

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Iced Tea

Carly’s sandwich cafĂ© serves the best iced tea in town. Their decaffeinated tea is caffeine-free as compared to their regular caffeinated tea. If a regular glass of iced tea is ounces, how many ounces of decaffeinated tea would you have … Continue reading

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Divisibility of Pythagorean Triples

1. Show that if are integers such that , then (a) at least one of them is divisible by (b) at least one of them is divisible by (c) at least one of them is divisible by . 2. Show … Continue reading

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Intersecting Circumcircles

The given in the above figure are: is a right triangle at is a right triangle at Points , and are collinear Points , and are collinear cm cm 1. (a) What is the measure of ? (b) Deduce from … Continue reading

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