A square containing a quarter circle and a tangent line segment. What is a : b?
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Buddha’s belly
Tag: triangle
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The stuck boulder
A rectangle contains a circle wedged between two triangles. What is the circle radius in terms of triangle heights a and b?
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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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The Queen’s chamber
A right triangle with three squares forming a smaller inner triangle. What is the maximal blue fraction?
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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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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 Holy Trinity
Three similar triangles are placed such that they form a large triangle. What is the proportion of line segments a : b?
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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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Two steps forward
Two equilateral triangles share a vertex and have their bases on the same line. A third equilateral triangle is constructed from their apexes. Prove that its apex is also on that line.