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Beginner

The full circle

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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Intermediate

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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Advanced

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?

Categories
Beginner

Down the tree

Two overlapping congruent isosceles triangles. What fraction of the total area is green?

Categories
Beginner

The leftover package

An isosceles triangle with an inscribed square and three triangles. What is the proportion black : red?

Categories
Intermediate

Jingle bells

Two equilateral triangles share a vertex. What is the area of their overlap region?

Categories
Advanced

The crowded house

Three circles are inscribed in a rectangle. What is the area X in terms of A and B?

Categories
Intermediate

Lost in rotation

Four equilateral triangles inscribed in a fifth one. What fraction of the latter is coloured?

Categories
Intermediate

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.

Categories
Beginner

The dog ear

A square contains a triangle. What fraction of the square is red?