Two circles, one having its centre on the other, and four line segments. Prove that the three coloured line segments are congruent.
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Hang a right
Tag: length
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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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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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Count to five
A triangle with a cevian. What’s α?
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The truss bridge
Two lines connected by five triangles. Prove that orange = blue. Created by Marshall W. Buck.
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The sandal
A triangle with two angular bisectors. What’s the proportion blue : red?
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Diamond life
Two equilateral triangles and one centre. What’s green : red?
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The Moroni minimum
An arbitrary point on the parabola y=x2. Shown are the tangent in that point and a line segment perpendicular to it. What is the minimal height h?