A square with a diagonal and a right triangle. What’s the proportion blue : red?

# Month: July 2022

## The steam locomotive

Two tangent circles, a chord towards the tangency point and a tangent. What’s the proportion a : b in terms of radii R and r?

## The inner circle

A triangle with its incircle. A line segment through two tangency points and one through the incentre. What’s the angle α?

## Know all angles

A triangle with its circumcircle and circumcentre. What’s α : β?

## True colours

In this right triangle, if red = blue, what is orange : purple?

## We are equal

A quadrilateral with its diagonals. What’s the angle α?

## A nice percentage

An orange square and a blue rectangle with two congruent inscribed circles. What is the angle α?

## The gremlin

Two circles and three coloured isosceles triangles. Prove that the circles are concentric.

## The Pappus eggs

Three semicircles and a circle with their centres. Two orange ellipses with focal points in the semicircle centres (they share the middle one). Prove that their upper intersection point coincides with the circle centre.

Three semicircles and a circle. Three centres are shown in green. What’s the proportion red : blue?