A cyclic quadrilateral and two diagonals. What fraction of its area is blue?
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Similar intention
Tag: circle
Four circles and a common tangent. The areas of the green and yellow circle are given. What are the areas of the red and blue circle?
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The flat earth
An observer is standing on a plane at h metres below the centre of a reflecting sphere of radius r. Another object on the plane is perceived at an angle α from the vertical. What is α of the horizon in terms of h and r?
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Z
A green quadrilateral of which two sides are tangent to a quarter circle of radius r. What is its area?
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Overlapping interests
A square, a rectangle and a circle that partially overlap. One square vertex coincides with a rectangle-circle tangency point. Prove that the area of the square equals that of the rectangle.
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The sliding square
A square of variable size inscribed in a semicircle of radius r. What is the maximum distance d of the lowest square vertex to the nearest semicircle corner?
A rectangle with two congruent circles, a semicircle and a common tangent. What is the proportion of side lengths a : b?
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The rising sun
A rectangle with a circle and a semicircle. What is the proportion red : blue in terms of a and b?
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The flying saucer
A quarter circle with four chords. What is the proportion purple : gold?
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The dance
A regular hexagon, two squares and a semicircle connecting two vertices. Is the red vertex located on the semicircle?