Two touching circles and two lines passing through the tangency point. What is the area proportion of the two triangles?
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The butterfly effect
Tag: circle
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Don Quixote and the windmill
Don Quixote is approaching a windmill. The sails of length √2 are attached to a point that is 2 above eye level. What is the maximum vertical angle that Don Quixote perceives as he moves forward?
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Beware of the dots
Two congruent circles and a common tangent. A triangle connecting tangency points and the upper intersection point. What angle α maximises its area?
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Radioactive material
A circle divided into six congruent sectors. A smaller concentric circle of radius one quarter of the large one. What fraction is black?
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The complicated jet
Two congruent squares inside a circle. The extended diagonals meet at the circle circumference. What’s their angle?
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The dark side
A quarter circle containing two touching semicircles cut by a chord. What fraction is brown?
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An Italian hill
Two semicircles inside a rectangle. What is the proportion of the red to the green area?
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The carambole
Three touching congruent circles inscribed in an equilateral triangle. A small equilateral triangle inscribed in the centre space. What fraction is blue?
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The eye of the beholder
A square and two equilateral triangles inside and touching a circle. What’s the angle α?
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The hunting horn
Two semicircles and four tangents. What’s the area of the orange rectangle?