128 Basic geometric constructions
Appendix: Some basic construction principles
Theorem 4.2(Perpendicular bisector locus).Given two distinctAand
Bon a plane, a pointPis equidistant fromAandBif and only ifPlies
on the perpendicular bisector of the segmentAB.
Theorem 4.3(Angle bisector locus).A pointPis equidistant from two
given intersecting lines if and only if it lies on the bisector of an angle
between the two lines.
Note that two intersecting lines have two angle bisectors.Theorem 4.4.If two circles are tangent to each other, the line joining
their centers passes through the point of tangency.
The distance between their centers is the sum (respectively difference)
of their radii if the tangency is external (respectively internal).