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?

# Month: December 2021

## 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?

## 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?

## Down the tree

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

## The leftover package

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

## Jingle bells

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

## The crowded house

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

## Lost in rotation

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

## 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.

## The dog ear

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