A rectangle with a diameter and two inscribed squares. What is its area in terms of the square areas A and B?
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The letter box
Category: Advanced
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A close encounter
Two semicircles are tangent to each other’s diameter. Are the line segments connecting their corners parallel?
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The extra large
A triangle with a cevian splitting its base in parts of length 2 and 1. What is the angle α?
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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 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 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 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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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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The earth projection
A circle touching a semicircle and a triangle. What is the proportion blue : green?
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Cordon sanitaire
Two perpendicular lines and a third line. Four circles are tangent to all three lines. Prove that their areas satisfy AB=CD.