Inequalities For Distances Between Triangle Centers
Abstract
In his seminal paper on triangle centers, Clark Kimberling made a number of conjectures concerning the distances between triangle centers. For example, if D(i; j) denotes the distance between triangle centers Xi and Xj , Kimberling conjectured that D(6; 1) ≤ D(6; 3) for all triangles. We use symbolic mathematics techniques to prove these conjectures. In addition, we prove stronger results, using best-possible constants, such as D(6; 1) ≤ (2 -3)D(6; 3).
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