Two squares of area D and J share a vertex while the circle passes through four other vertices. What is the area of the latter in terms of D and J?
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The full circle
Month: December 2021
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The residue
A parabola is tangent to two sides of a square and to the hypotenuse of an isosceles triangle. The three tangency points are shown. What fraction of the square is green?
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Mind the gap
A regular hexagon with an equilateral triangle sharing a vertex and having a vertex somewhere along the opposite side. What is the maximum length of line segment g?
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Down the tree
Two overlapping congruent isosceles triangles. What fraction of the total area is green?
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The leftover package
An isosceles triangle with an inscribed square and three triangles. What is the proportion black : red?
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Jingle bells
Two equilateral triangles share a vertex. What is the area of their overlap region?
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The crowded house
Three circles are inscribed in a rectangle. What is the area X in terms of A and B?
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Lost in rotation
Four equilateral triangles inscribed in a fifth one. What fraction of the latter is coloured?
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Pulling the strings
Two rods of length x and y are connected by two strings with a knot exactly halfway. The rods are placed parallel both with uncrossed and crossed strings. The distance between the knots is measured as a and b respectively. Express x and y in terms of a and b.
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The dog ear
A square contains a triangle. What fraction of the square is red?