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Blazing hot

A circle inscribed in a triangle inscribed in a semicircle. The line segment through two tangency points meets a radius at the semicircle circumference. What is the angle α?

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Solution

The angle α is 45°.

Solution by Dr Rick.
Incircle formula by Dr Rick.

Visual proof

Proof without words by David Andriana.

Poem

Blazing hot
A volcanic eruption
A fantastic flow
A river of fire ans thunder
Scent from the heavens
Lava sculpts the landscape
The mountain is crying once more
Burning in its core
A big change for the landscape
Where everyone wants to escape
The mountain blows up and is awake

Bella

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