Area of an Inscribed Triangle in Terms of the Product of Its Sides
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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.
Contributed by: Tomas Garza (October 2019)
Open content licensed under CC BY-NC-SA
Details
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.
Reference
[1] A. Bogomolny. "Metric Relations in a Triangle." (Oct 8, 2019) www.cut-the-knot.org/triangle/MetricRelationsInTriangle.shtml.
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