Category: Triangle inequalities

List of triangle inequalities
In geometry, triangle inequalities are inequalities involving the parameters of triangles, that hold for every triangle, or for every triangle meeting certain conditions. The inequalities give an orde
Pedoe's inequality
In geometry, Pedoe's inequality (also Neuberg–Pedoe inequality), named after Daniel Pedoe (1910–1998) and Joseph Jean Baptiste Neuberg (1840–1926), states that if a, b, and c are the lengths of the si
Hadwiger–Finsler inequality
In mathematics, the Hadwiger–Finsler inequality is a result on the geometry of triangles in the Euclidean plane. It states that if a triangle in the plane has side lengths a, b and c and area T, then
Weitzenböck's inequality
In mathematics, Weitzenböck's inequality, named after Roland Weitzenböck, states that for a triangle of side lengths , , , and area , the following inequality holds: Equality occurs if and only if the
Ono's inequality
In mathematics, Ono's inequality is a theorem about triangles in the Euclidean plane. In its original form, as conjectured by T. Ono in 1914, the inequality is actually false; however, the statement i
Euler's theorem in geometry
In geometry, Euler's theorem states that the distance d between the circumcenter and incenter of a triangle is given by or equivalentlywhere and denote the circumradius and inradius respectively (the
Erdős–Mordell inequality
In Euclidean geometry, the Erdős–Mordell inequality states that for any triangle ABC and point P inside ABC, the sum of the distances from P to the sides is less than or equal to half of the sum of th
Barrow's inequality
In geometry, Barrow's inequality is an inequality relating the distances between an arbitrary point within a triangle, the vertices of the triangle, and certain points on the sides of the triangle. It