A square is fitted into an equilateral triangle as shown. What fraction is shaded?
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The square peg
Author: Rik D. Tangerman
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The Pacman principle
In a circle, two congruent chords are connected in a point. A line segment is drawn through the circle center as shown, forming two angles. What is the proportion α : β?
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The velocipede
Two circles are embedded in a frame of size 9 x 8. What is their total area?
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The blue diamond
Two isosceles triangles are placed as shown. What is the proportion of the line segments a and b?
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The askew envelope
In a square, an interior point is drawn with an angle to the top vertices of 120°. What’s the angle between the chords formed by the two arcs centered in these vertices?
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The fishing net
Two squares and two equilateral triangles. What fraction is hatched?
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The lazy spider
A spider situated at point A on the outside of a cylinder with diameter 4 and height 3 is trying to get to a fly at point C on the complete opposite side as fast as possible. What is the shortest route?
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The inner wheel
A wheel is placed inside another that has exactly twice its radius. If the inner wheel rolls around once without slipping, how many revolutions has it completed?
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The broken window
A square is divided into triangles and quadrilaterals as shown. What fraction of the square area is covered by the shaded triangle?
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The shark fin
An isosceles triangle is inscribed in a semicircle with one side along the diagonal and the top vertex somewhere on the semicircle. What’s the maximum fraction shaded?