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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

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