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 ball pool
Month: November 2021
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Square eyes
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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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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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 life net
The vertices of a regular hexagon are connected to midpoints of opposing sides. What fraction is red?
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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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Below the line
Two squares share a vertex at the origin and have their sides along the x- and y-axis. Two vertices lie on the line satisfying x+2y=c. What is the proportion purple : yellow?
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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?