A circle with its centre in the origin is cut by two parallel lines that are a distance d apart. One line is passing through the leftmost and one through the lowest point of the circle. What is the area of the green trapezium in terms of d?

# Month: October 2021

## The Holy Trinity

Three similar triangles are placed such that they form a large triangle. What is the proportion of line segments a : b?

## The blue wink

A semicircle inscribed in a triangle inscribed in a semicircle. What fraction of the total area is blue?

## Kindergarten

A circle with three tangents and two squares. The accentuated vertex is a tangency point. What’s the angle α?

## Life is a dance

A quarter circle inside a square divides a line segment in parts of length 4 and 6. What is the square’s area?

## Colour confinement

A semicircle with three tangent line segments. What is its area in terms of lengths a and b?

## Two steps forward

Two equilateral triangles share a vertex and have their bases on the same line. A third equilateral triangle is constructed from their apexes. Prove that its apex is also on that line.

## The earth projection

A circle touching a semicircle and a triangle. What is the proportion blue : green?

## Crazy frog

A regular pentagon, two semicircles and two chords. What’s the length proportion a : b?

## Composition in red, blue and yellow

A rectangle containing red and blue squares and a yellow rectangle. What is the proportion red : (blue+yellow)?