Two circles and three coloured isosceles triangles. Prove that the circles are concentric.
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The gremlin
Tag: triangle
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The wall socket
Two equilateral triangles share a vertex. Prove that their centres and the highlighted vertex are collinear.
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Fair and square
Two squares of which three vertices form an isosceles triangle. What is the angle α?
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The golf ball
A circle and a triangle with two sides tangent to the circle and a side connecting the tangency points. The line segment of the circle centre to the triangle apex is shown. Prove that α = β.
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The triangle pull
An equilateral triangle with given distances between its vertices and an exterior point. What’s its side length x?
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The rotary movement
Two arbitrarily placed congruent equilateral triangles. Out of all the possible rotations of the plane, for how many will the image of ABC be A’B’C’?
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Three folds
A square divided by three line segments. What’s the proportion yellow : purple?
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Opposing camps
A square containing two overlapping equilateral triangles. What’s the length proportion a : b?
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Spiegel im Spiegel
A triangle with an inscribed triangle. What fraction of the former does the latter cover in terms of lengths a, b, c, d, e and f?
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The lever of Archimedes
Two congruent triangles are placed as shown. A line segment passes through the centroid of the yellow triangle. What’s the proportion a : b?