Two regular pentagons share a vertex. What’s the angle α?
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Tipping point II
Tag: angle
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Drilling site
A blue flagpole is erected near a drilling site. Lines are drilled perpendicular to the flagpole guy wires and meet at the bottom of the orange drilling pipe. What is the ratio of distances green to red?
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Cathedral on the hills
A cathedral is erected on two hills, the side circular arcs whose centers are the hill ends, and so that the right (and left) side arcs are orthogonal. Show that the tip of the spire is directly above where the hills meet.
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Triangulation
A regular dodecagon contains a yellow square. Find the three angles α, β and γ.
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Flying saucer II
If X is the midpoint of the segment connecting the centers of the upper and lower arcs, and JK is perpendicular to XH, then show that H is the midpoint of JK.
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Miniaturisation
Two tangent circles and two common tangents. A and D are centres. B is midpoint of AD. C is midpoint of BE. What is the angle α?
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The Siamese triplet
Three circles with a common intersection point and two triangles. What is α : β?
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Wheel in motion
A circle with its centre and two squares sharing a vertex. What’s the angle α?
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Distant Alp II
A square with its diagonal. Prove that the three red points are collinear.
Blue and orange concentric circles intersect a vertical line in green dots. Show that the dots are equally spaced, given that the red intervals shown are of equal length. (The largest circle has radius 2u.)