Prove that the centre of a circle touching two intersecting lines lies on the angle bisector of the lines.

Find the locus of centres of circles which touch two intersecting lines.

Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection

Prove that the line of centres of two interesting circles subtends equal angles at the two points of intersection.

A circle (with centre at O) is touching two intersecting lines AX and BY. The two points of contact A and B subtend an angle of 65^(@) at any point C on the circumference of the circle. If P is the point of intersection for the two lines, then the measure of angle APO is :

Two chords AB and AC of a circle are equal. Prove that the centre of the circle lies on the angle bisector of /_BAC.

Two chord AB and AC of a circle are equal. Prove that the centre of a circle lies on the angle bisector of /_BAC

Prove that two lines that are respectively perpendicular to two intersecting lines intersect each other.

Prove that two lines that are respectively perpendicular to two intersecting lines intersect each other .