Categories

## A fair division

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

Categories

## 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?

Categories

## 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?

Categories

## Know all angles

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

Categories

## True colours

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

Categories

## We are equal

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

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## A nice percentage

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

Categories

## The gremlin

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

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## 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.

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## The chain

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