| Manifesto | Bookstore | Contents | Amazon store | Term index | What changed? | Contact | Recommend |
Optimization Problem in Acute Angle: What is it about?
|
| Buy this applet What if applet does not run? |
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 |
Let AB and AC be the reflections of A in the sides of the angle. Then the perimeter of 
ABC 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.
References
- V. M. Tikhomirov, Stories about Maximua and Minima, AMS & MAA, 1990
- I. M. Yaglom, Geometric Transformations I, MAA, 1962
| 34222801 |  |
