A regular hexagon, a square and a rectangle. What is the area proportion rectangle : square?
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Squaring a rectangle
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A clear vision
A circle containing a regular pentagon and two equilateral triangles. All shown points are on the circle. What’s the angle α?
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Star and stripes
Two concentric congruent squares and two red rectangles. What fraction of the total area is red?
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The inner parallel
A cyclic quadrilateral with its diagonals and two altitudes. Prove that AB is parallel to EF.
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Letting go
Two squares share a vertex. Three other vertices are collinear. What is the area proportion of the blue to the red square?
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Orange above
A square contains a right triangle. What fraction is orange?
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The double flag
Three tangent circles and a common tangent. The three tangency points are shown. What is α + β?
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The door stop
A triangle with a cevian. What is α?
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Four to twelve
A regular dodecagon and a square share two vertices. What is the area proportion square : dodecagon?
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The japanese progression
An isosceles trapezium with its inscribed circle. If the lengths are such that b-a=c-b=d-c, what is a : b : c : d?