An equilateral triangle with a cevian and two inscribed circles. What is yellow : red?
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Compartments
Category: Intermediate
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Communicating vessels
A semicircle and two squares. What is the blue area in terms of a and b?
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Crossing straps
Every side of a quadrilateral is divided into three equal parts. What is purple : orange?
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The Grand Fir
A triangle, its circumcircle, circumcentre and two altitudes. What’s the angle α?
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Stretch of imagination
Four squares are placed as shown. Prove that the green quadrilateral is a parallelogram.
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Lunar ratios
A circle of radius r is interior-tangent to the larger yellow circle of radius R, with diameters overlapping. Express s/k in terms of r and R.
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Construct the ladder
Two rays emanating from point A and a point B between them. Construct the line segment that has an endpoint on each ray and its midpoint in B using a tool such as GeoGebra, explaining your steps.
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The shadow side
A triangle with sides of length a and c is divided by a cevian of length b. What is brown : yellow in terms of a, b and c?
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Communication across the void
The end points of three diameters of three circles are involved in two cyclic quadrilaterals, purple and orange, separated by the green triangle. What is the angle α between the other (not diameter) diagonals of the two quadrilaterals?
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Slippery slope II
The V is symmetric with respect to the vertical. Prove the algebraic relationship between the various segment lengths indicated by letters.