CBSE Class 10 Answered

let the circle touch one line at A and the other at B.

then if O is the center of the circle,

then OA and OB  have to  be perpendicular to the respective lines.

since OA  and OB   are the radii of the same circle,

 OA=OB

thus,

 O is equidistant from the lines

 thus, using the definition of angle bisector that i'ts a set of points equidistant from the arms of the angle,

 we conclude that O lies on the angle bisector of the angle between the two intersecting lines.