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Triangle angles

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Given triangle ABC with no angle >120 degrees, find and construct the point P for which PA + PB + PC is a minimum. What is this point called? What would be the case for a triangle with an angle of 120 degrees or more?

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Solution Summary

This shows how to construct a point in a triangle with given characteristics.

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Step 1:Draw the triangle A, B, C
Step 2: Construct on every side of the triangle an equilateral triangle. By this procedure the points A*, B*, C* are generated.
Step 3: Connect each of the newly constructed points A*, B*, ...

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