A square with an extended side. What’s the angle α?
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Ice cube II
Author: Rik
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Along similar lines
The blue triangle is similar to the green one and has the same orientation. The midpoints between corresponding vertices are connected to form a red triangle. Prove that it is also similar.
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Methane
Four orange unit circles and their red centres. What is the radius of the green circle? Kindly provided by Marshall W. Buck.
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Rule of 72
Two triangles and an extended side. What’s blue : orange?
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The bubble chamber II
A square with a diagonal and two circles. What is the area proportion of the two circles?
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Sailing by night
A circle with an inscribed quadrilateral. Prove that ab=cd. Kindly provided by Marshall W. Buck.
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The hawfinch II
A circle with two tangents. What’s red : blue in terms of α?
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Outside the frame
Two squares and an equilateral triangle. Prove that the area of the triangle plus the small square equals that of the large square.
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The odd balance
Two circles are tangent to two perpendicular lines and have their centres connected. Prove that the green triangle is right isosceles.
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The stack
Three squares and three line segments. What’s the angle α?