A semicircle, a square and an isosceles triangle. What’s the angle α?

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## Solution

The angle α is 22,5°.

First look at isosceles triangles GED and GCD. A simple matter of angle chasing reveals that angle CGE is 45°.

Now triangle GBC is also isosceles, because Thales implies its top corner is 90°. Therefore BC=GC. It also implies that 180-2β=135 and therefore β=22,5°.

Next, using SAS, one can show that triangles GCD and BCF are congruent. Since triangle BCF is now isosceles, we have 45-α=β and hence α=22,5°.

## Poem

The eightfold path

A way leading to liberation

While practising meditation

And try to do the right actions

In buddhism the work between body and spirit in union

Working on qualities like

Kindness and compassion

A kind of middle way

Between contemplation

And intentions