(a) The locus of a point equidistant from a fixed point is a circle with the fixed point as centre.
(b) The locus of a point equidistant from two interacting lines is the bisector of the angles between the lines.
(c) The locus of a point equidistant from two given points is the perpendicular bisector of the line joining the points.
- null - Theorems Based on Loci
Describe the locus for questions 1 to 13 given below:
1. The locus of a point at a distant 3 cm from a fixed point.
In triangle LMN, bisectors of interior angles at L and N intersect each other at point A. prove that:
(i) Point A is equidistant from all the three sides of the triangle.
(ii) AM bisects angle LMN.
Draw an ∠ABC = 60°, having AB = 4.6 cm and BC = 5cm. Find a point P equidistant from AB and BC; and also equidistant from A and B.