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Intermediate

Sisyphus

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

Solution by Jane Miller.

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

Bella

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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?

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