A regular pentagon and two squares. Prove that the four purple vertices are concyclic.
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Squaring the miter
Tag: pentagon
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Eye of Providence
A regular pentagon and an equilateral triangle. What is the angle α?
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Miracle multiplication with pentagons
Seven regular pentagons connect as shown. Show that C is the midpoint of the line segment FS.
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Average point constuction
Given a way of finding the midpoint of any segment (and connecting points to make lines, and intersecting lines to get points), construct the average of 5 points, using only 4 midpoint constructions. (Shown is a method using 5.)
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Miquel’s star
A convex pentagon ABCDE with extended sides and five circles connecting vertices and intersections. Prove that FKBMI are concyclic. Bonus question: prove KLMNO concyclic.
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Centre of attraction II
A square and a regular pentagon share a vertex. The square centre is a vertex of the pentagon. What’s the angle α?
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Meeting in the pentagon
A regular pentagon and two right angles. What is the angle α?
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Circular tension
The orange circle is a locus of points with constant sum of square distances from the vertices of a pentagon ABCDE; I.e., |GA|2 + |GB|2 + …+ |GE|2 is a constant. What is the center of the circle?
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The dumbbell
A square and two regular pentagons. What is red : yellow?
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Jacob’s Ladder
A regular pentagon with two extended sides. What is a : b : c?