Two tangent circles and two red tangent line segments. The three tangency points are shown. What is the angle β in terms of the angle α?
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The French kiss
Tag: circle
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Stuck in the middle
A right triangle with semicircles along its perpendicular sides having lengths a and b. Two smaller inscribed circles. What is the proportion blue : red in terms of a and b?
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The intersection
Two intersecting circles. Prove that the three blue line segments are of equal length.
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All the marbles
A circle containing eight touching circles. Circles of equal colour are congruent. What fraction of the total area is coloured?
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The drunk spider
A circle with several chords forming four coloured triangles. What is the proportion yellow : purple?
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Two square pegs
Two squares and a circle. What is the proportion a : b?
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Eye of the apple
A circle with an inscribed triangle with an inscribed circle. The centre of the large circle is on the small one. What fraction of the area is blue?
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The other half
Three semicircles with diameters a, b and x. Express x in terms of a and b.
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The Gouda cheese
A quarter circle with two inscribed squares. What’s the angle α?
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The ice cream cone
A circle tangent to a triangle side and to the two other extended sides. What is its diameter?