A square with four quarter circles of which the intersection points are the vertices of a yellow quadrilateral. What fraction of the total area is yellow?
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Square eyes
Tag: circle
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The outsider
A circle with an inscribed regular pentagon, a square and a triangle. Prove that the point lies on the circumference of the circle.
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Black hole sun
A square containing two quarter circles and a common tangent. What is the proportion yellow : black?
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My two cents
A right triangle is divided in two triangles, one of which is isosceles. The two inscribed circles are congruent. What is the total area?
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The lunar twins
Three circles are tangent to each other. The black chords go through their tangency points. Prove that the red chord is a diameter of the largest circle.
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The red planet
A semicircle with a chord and a line segment perpendicular to it. What is the total area in terms of lengths a and b?
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The green trap
A circle with its centre in the origin is cut by two parallel lines that are a distance d apart. One line is passing through the leftmost and one through the lowest point of the circle. What is the area of the green trapezium in terms of d?
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The blue wink
A semicircle inscribed in a triangle inscribed in a semicircle. What fraction of the total area is blue?
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Kindergarten
A circle with three tangents and two squares. The accentuated vertex is a tangency point. What’s the angle α?
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Life is a dance
A quarter circle inside a square divides a line segment in parts of length 4 and 6. What is the square’s area?