A square divided by three line segments. The red and blue areas are equal. What’s the length proportion a : b?
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Check and balance
Author: Rik D. Tangerman
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The dolphin
Two semicircles, a tangent and an altitude to the tangency point. Prove that the red triangle is isosceles.
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Extreme parallelism
Four parallel line segments, one of which is divided in three parts. What is the proportion blue : red : green?
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Parallelism
A trapezium with its diagonals and a parallel line segment. What’s the proportion blue : red?
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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.