A quarter circle inside a square divides a line segment in parts of length 4 and 6. What is the square’s area?
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Life is a dance
Tag: area
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Colour confinement
A semicircle with three tangent line segments. What is its area in terms of lengths a and b?
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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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Composition in red, blue and yellow
A rectangle containing red and blue squares and a yellow rectangle. What is the proportion red : (blue+yellow)?
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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.
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The green zone
A quarter circle and a right triangle inside a square. One of the vertices of the triangle is the square’s centre. What fraction of the square’s area is green?
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The kissing circles
A rectangle with three touching quarter circles. What fraction of its area is coloured?
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The balancing act
A square with two perpendicular lines. What is the minimal blue fraction?
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The commons
Two touching circles and a common tangent. Three triangles are formed by tangency points and centres. What is the area of the green triangle X in terms of areas A and B?
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Softening the edges
A quarter circle contains a semicircle and a square. What fraction of the area is purple?