Three small right triangles embedded in a large right triangle. Two of the areas are given. What’s the area of the smallest one?
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The baby brother
Author: Rik D. Tangerman
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The tumbler doll
A circle within an equilateral triangle within a circle. What fraction is shaded?
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The King’s chamber
A pyramid with a square base and sides that are equilateral triangles contains a cube. If the cube is taking maximum space as shown, what is the fraction of its volume to the pyramid’s volume?
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The sundial statement
A triangle is formed by a circle radius and an external point. It is divided by the shown chord. What’s the proportion of the angles α and β?
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The folded triangle
An equilateral triangle is folded with its left side at right angles with the base. What fraction of the total triangle is shaded?
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The green kimono
An equilateral triangle and three squares. What’s the angle?
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The wheelbarrow
A circle and two semicircles are nested as shown. What’s the proportion of their respective radii a : b : c ?
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The circus tent
A regular octagon is coloured as shown. What fraction of its area is red?
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The party hat
A cone has height 6 and base diameter 6. On it lie two points, one exactly halfway up, the other diametrically opposed at the base. What’s the shortest distance between these points going along the cone surface?
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The windshield wipers
A square and two rectangles, connected by two circular arcs, form a square. What is the proportion of the orange to the green area?