Three squares and four extended sides. What is the yellow area X in terms of blue and green areas A and B?
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The square telescope
Category: Intermediate
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The tipping point
Two touching circles, two diameters and two common tangents. What is the area of the green quadrilateral in terms of radii x and y?
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The crown
Three triangles have the same base. What is the top angle γ of the middle one in terms of the other ones α and β?
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Angles galore
Two triangles share a side. What’s the angle β?
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The wall between us
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 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?