There are four possible squares with a vertex at distance a from the centre and two vertices on the circle of radius r. Find their areas in terms of a and r.
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Ruyles squares
Month: December 2022
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Pushing the boundary
Two equilateral triangles are placed side by side. What’s the proportion green : red?
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The Pyramid of Austerlitz
An equilateral triangle and a parabola that is tangent to two of its sides in two vertices. Proof that the triangle centre coincides with the parabola focus.
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The skewed tree
A triangle with a line segment through its centroid and parallel to a side. What faction is dark green?
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A deep connection
Two squares inside a circle. What is the circle area in terms of length a?
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Square one
Three squares share a vertex. Two line segments pass through side midpoints. Prove that a : b = c : d.
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To shy away
Two squares share a vertex. What’s the proportion orange : blue?
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The domino effect
Two overlapping congruent rectangles. What’s the angle α?
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Squaring a rectangle
A regular hexagon, a square and a rectangle. What is the area proportion rectangle : square?
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A clear vision
A circle containing a regular pentagon and two equilateral triangles. All shown points are on the circle. What’s the angle α?