A circle inscribed in a triangle inscribed in a semicircle. The line segment through two tangency points meets a radius at the semicircle circumference. What is the angle α?
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Blazing hot
Three squares are placed as shown. What fraction of the total area is green?
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The turning point
Two isosceles triangles share a vertex. What is the maximum of their area proportion red/green?
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The kingsize bed
A rectangle with an inscribed right triangle. What is ac/bd?
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The obstructed view
A rectangle and two squares of side length a and b respectively. What is the red area in terms of a and b?
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Mickey Mouse
Three regular pentagons and two extended sides. What fraction of the total area is red?
A square containing a rectangle and a tangent quarter circle. What fraction is orange?
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Camera obscura
A quarter circular room is covered with mirrors. A ray of light is emitted from one corner and reflected somewhere on the opposite wall, then on the arc, before reaching the adjacent wall at a point a distance a from the light source and b from the circle centre. What is the maximum of a/b?
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The pine forest
A square containing a quarter circle. What’s the proportion blue : brown : green?
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The freight elevator
Four points A, B, C and D form a quadrilateral. Prove that it is a rectangle if and only if for an arbitrary point P we have PA2+PC2=PB2+PD2.