Two congruent rectangles and squares. Proof that the four points are on one circle.
Author: Rik D. Tangerman
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The pentagon push
Two regular pentagons share a vertex. What’s the angle α?
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En garde
An isosceles triangle with two altitudes dividing each other in segments of length 4 and 5. What is the total triangle area?
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The satellite
A circle containing three squares. What fraction is coloured?
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Distant peaks
Two isosceles triangles and a right angle. What is the proportion green : gold?
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The blue pill
A regular octagon containing a blue hexagon. All line segments have equal length. What fraction is blue?
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The Lion King II
A regular hexagon and three squares. What is the proportion yellow : brown?
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The eye mask
A right triangle with its inscribed circle. Two cevians are drawn through the circle centre. What is the circle area in terms of triangle areas A and B?
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The red balloon
An equilateral triangle with an altitude. Two of its sides form the radii of the circular sector. What fraction of the area is covered by the red circle?
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The dangling square
Four squares and five shared vertices. If the orange area is 4, what is the green area?