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

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.