Pedoe's inequality
In geometry, Pedoe's inequality states that if a, b, and c are the lengths of the sides of a triangle with area f, and A, B, and C are the lengths of the sides of a triangle with area F, then
- <math>A^2(b^2+c^2-a^2)+B^2(a^2+c^2-b^2)+C^2(a^2+b^2-c^2)\geq 16Ff,<math>
with equality if and only if the two triangles are similar.
References
- "A Two-Triangle Inequality", D. Pedoe, The American Mathematical Monthly, volume 70, number 9, page 1012, November, 1963.
- "An Inequality for Two Triangles", D. Pedoe, Proceedings of the Cambridge Philosophical Society, volume 38, part 4, page 397, 1943.
