A square diagonal is divided in three by a 45-degree angle. Two pieces are given, what is the length of the third?
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The divided diagonal
Author: Rik D. Tangerman
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The dark side
A quarter circle containing two touching semicircles cut by a chord. What fraction is brown?
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The parquet floor
A unit rhombus is surrounded by four congruent parallelograms. All five quadrilaterals have equal area. What are the parallelogram sides x and y?
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New Year 2021
Three squares are placed as shown. Given that the green areas are equal, what is the side length of the orange square?
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An Italian hill
Two semicircles inside a rectangle. What is the proportion of the red to the green area?
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Domino day
Three congruent rectangles consisting of two squares each are placed as shown. What is the blue area?
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The carambole
Three touching congruent circles inscribed in an equilateral triangle. A small equilateral triangle inscribed in the centre space. What fraction is blue?
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The eye of the beholder
A square and two equilateral triangles inside and touching a circle. What’s the angle α?
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The star of Bethlehem
Two concentric equilateral triangles with parallel sides. What fraction is orange?
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The christmas tree
A triangle, a median and another cevian. What is the proportion of the two areas?