Five congruent rectangles. What’s their proportion width : height (aspect ratio)?
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The brick oven
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Inside the box II
A square contains four other squares. Prove that the red line segment is parallel to its vertical sides.
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Decorating the tree
A symmetric tree has decorative lines of equal slope, and of lengths 11 and 13. What is the area ratio of green to red to brown?
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The brick pile
Three congruent rectangles inscribed in a triangle. What fraction is brown?
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The mis-stacked trays
A rectangle is turned 90°, bisecting a bigger rectangle of the same shape. When squares are removed from the two side pieces, the remaining rectangles have the same shape as well. What is the common ratio of the rectangle side lengths?
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Compartmentalization
A square with two circles and two common tangents. What’s red : blue?
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Scratching the surface II
Two equilateral triangles, the smaller one being of variable size. What is the minimum value of orange : blue?
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Land and sea
Two circles, some triangles, and a blue tangent line to the orange circle. Show that the two green triangles are similar.
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Inside the box
Two squares inside a square share a vertex. What’s the angle α?
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Through the roof
A semicircle with its centre. What is green : red in terms of the angles α and β?