Arbelos' Morsels

What is this about?

A Pleasant Fact

Assume $B'C=BC\;$ and that all the curves that appear in the diagrams below are semicircles.

Arbelos' Morsels

Then in each diagram the areas of different colors are equal.

Proof

The proof is left as an exercise.

Acknowledgment

I am grateful to Teo López Puccio from Argentina for sharing his observation of this configuration related to the famous arbelos.

 

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