Area of an Inscribed Triangle in Terms of the Product of Its Sides

The area of a triangle inscribed in a circle of diameter 1 can be expressed in terms of the product of its three sides. This Demonstration presents a step-by-step derivation of this result.


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This is one of many interesting results concerning triangles. An impressive list appears in [1].
A detailed step-by-step derivation for this particular case may be useful for geometry amateurs, and the source code provides some tips for geometric drawing with the Wolfram Language.
[1] A. Bogomolny. "Metric Relations in a Triangle." (Oct 8, 2019)
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