A semicircle containing two circles and two triangles. The blue right triangle connects three tangency points. Prove it is isosceles.

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## Solution

## Poem

The myth of Sisyphus

This legendary sisyphus

Obliged to roll his stone

With courage and dignity

On the mountain top

A mythical ascent

Rolling his stone painfully

Such was his destiny

Never a victory

Like a night of Gethsemani

For all it’s life

A never ending tragedy

## 2 replies on “Sisyphus”

I think you need to specify somehow that the smallest circle is at the midpoint of the side of the larger triangle to which it is tangent.

Why are the endpoints of the hypotenuse of the blue triangle and the point where the left cathetus touches the incircle of the great triangle colinear?