Optimization Problem in Acute Angle
What is it about?
A Mathematical Droodle
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This one is reminiscent of Heron's problem.
Let a point A lie in the interior of an acute angle. Find points B and C on the sides of the angle (one per side) such that the perimeter of ΔABC is minimal.
Let AB and AC be the reflections of A in the sides of the angle. Then the perimeter of ΔABC equals
AB + BC + CA ≠ ABAC.
The equality is achieved when B and C are chosen to be the points of intersection of the corresponding sides of the angle with ABAC.
- V. M. Tikhomirov, Stories about Maximua and Minima, AMS & MAA, 1990
- I. M. Yaglom, Geometric Transformations I, MAA, 1962