A quarter circle with two chords of given length. What is the area of the orange quadrilateral?
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The quarter trampoline
Tag: circle
From the purple triangle ABC and the center of its inscribed circle at D, form the three colored circles (BDC), (CDA), and (ADB), with centers F, G, H, respectively, thus forming the yellow triangle FGH. Prove that there is one circle that circumscribes both triangles.
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Alien mothership attacks dome city
Two semicircles with parallel bases. Show that HF and GE intersect on the perpendicular line to AC above A.
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The maternal bond
Three tangent semicircles and a circle. One tangency point is shown. Prove that red : green = yellow : blue.
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The cocktail
A triangle with two circles and two line segments. Prove that it is isosceles.
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Voting eccentric
A square with a circle and a tangent. The tangency point lies on the diagonal. What fraction is red?
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The bike chain
A square containing a semicircle, a circle and two tangents. What’s the angle α?
A triangle and two semicircles. What’s the angle α?
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Hang a right
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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Methane
Four orange unit circles and their red centres. What is the radius of the green circle? Kindly provided by Marshall W. Buck.