A trapezium with its diagonals and a parallel line segment. What’s the proportion blue : red?
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Parallelism
Author: Rik D. Tangerman
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Squaring the circle
Two perpendicular squares inside a circle. The circle centre is located on the side of one square. The line segment connecting two vertices has length a. What is the circle area?
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The inner diamond
A triangle with side lengths a and b and an inscribed rhombus. What is the blue fraction in terms of a and b?
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The Common Brimstone
A square divided by three line segments. What’s the proportion green : yellow?
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Silent circle
A large triangle with one side tangent to a circle. The tangency point is the vertex of a blue parallelogram. What is the red area?
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The yardstick
A rectangle containing a circle and a line segment connecting the top side to the bottom tangency point. What is its area in terms of lengths a and b?
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The Arcus arcade
A semicircle and an inscribed circle. Prove that the circle centre is on the parabola.
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The Suresh similarity
Two squares and a rectangle. Prove that the red triangles are similar.
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Tension control
Three squares and a line segment of which a vertex is the midpoint. What is the proportion purple : green?
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A new slant
Two squares and a slanted rectangle share three vertices. What is the total area?