Geometric inequalities (other)

Geometric inequalities are statements comparing geometric quantities (like lengths, areas, angles) that are always true under certain conditions. 'Other' geometric inequalities refer to those that do not fall under the most famous ones (like the triangle or Cauchy-Schwarz inequalities), but still provide useful bounds in geometry problems. Examples include inequalities involving the inradius, circumradius, medians, altitudes, or distances in polygons.

Important properties

• Geometric inequalities often relate different elements of a figure, such as sides and angles.

• They can help estimate or bound unknown quantities in geometry problems.

• Many inequalities are sharp, meaning equality holds only in special cases (often regular or symmetric figures).

• Proofs may use algebraic manipulation, geometric transformations, or known inequalities.