Two circles inscribed an a trapezium divided by a perpendicular line segment. What is the proportion of its length a and the side b?
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The wall between us
Category: Intermediate
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The minor chord
Three chords meet at the same point on the circumference of the circle. A perpendicular line segment divides one of them in two parts of length a and b. Express the length of the smallest chord x in terms of a and b.
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The bubble chamber
A regular hexagon and two semicircles connecting vertices. What’s the angle α between the chords?
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The ball pool
A square having side length 12 contains a quarter, semi and full circle. The centres of the latter two are connected to the square’s centre to form a green triangle. What is it’s area?
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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 ocean view
Two squares of variable size share a vertex. What is the maximal blue fraction?
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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?