Question

The locus of the centres of all the circles, which are tangents to the arms AB and BC of angle ABC is ______.

Options

• perpendicular bisector of arm AB

• perpendicular bisector of arm BC

• bisector of angle ABC

• none of these

Answer 1

The locus of the centres of all the circles, which are tangents to the arms AB and BC of angle ABC is bisector of angle ABC.

Explanation:

From figure,

PD = PE (Radius of circle with center P)

P'F = P'G (Radius of circle with center P')

∴ The centers of circles are equidistant from the lines AB and BC.

We know that,

The locus of a point equidistant from two intersecting lines is the bisector of the angles between the lines.

∴ The locus of the centers of all circles, which are tangents to the arms AB and BC of angle ABC is the bisector of angle ABC.