Two squares and two equilateral triangles. What fraction is hatched?
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The fishing net
Month: November 2020
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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?
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The diagonal dilemma
On two faces of a cube a diagonal is drawn that meet in the same vertex. What’s the angle between them?
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The blockhat
Four congruent rectangles are placed in a hat-shaped configuration. What’s the angle between the lines connecting the opposite corners?
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The corner pocket
A snooker player wants to corner a ball starting from a point on one side and bouncing two times from the opposite sides. Given the dimensions of the table in the figure, what’s the length of the track the snooker ball travels?
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The snowman mansion
A square and a half square are stacked in order to form a house-shaped quadrilateral. Inside two circles are closely packed. What’s the angle between the tangency points?
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Balancing balls
Two touching circles are placed on top of a right triangle. What’s the angle between the chords connecting the tangency points?