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
