AoPSWiki

Want to learn how to tackle those tough MATHCOUNTS and AMC counting and probability problems? Check out Art of Problem Solving's Introduction to Counting & Probability by David Patrick.

Personal tools

Search

Toolbox

Equidistant

From AoPSWiki

Equidistant means "at the same distance."

Thus, for instance, if triangle $\triangle ABC$ is isosceles with base $BC$ , points $B$ and $C$ are equidistant from point $A$ .

Similarly, the perpendicular bisector of a line segment is the set of points equidistant from the endpoints. So, given segment $\overline{AB}$ and a point $C$ such that $AC = BC$ , we know (by definition) that $C$ is on the perpendicular bisector of $\overline{AB}$ . Also, given $C$ on the perpendicular bisector of $\overline{AB}$ , we know that $AC = BC$ .

This article is a stub. Help us out by expanding it.

Retrieved from "http://www.artofproblemsolving.com/Wiki/index.php/Equidistant"

Categories: Stubs | Geometry

Try our innovative online adaptive learning system, Alcumus.
Over 1100 problems and 60+ video lessons. FREE!

© Copyright 2008 AoPS Incorporated. All Rights Reserved. • Foundation • Privacy • Contact Us