P is a point equidistant from two lines l and m intersecting at point A (see Fig. 7.38). Show that the line AP bisects the angle between them.

P is a point equidistant from two lines l and m intersecting at a point A , Show that A P bisects the angle between them.

AD and BC are equal perpendiculars to a line segment AB (see Fig. 7.18). Show that CD bisects AB.

Two parallel straight lines are inclined to the horizon at an angle prop . A particle is projected from a point mid way between them so as to graze one of the lines and strikes the other at right angle. Show that if theta is the angle between the direction of projection and either of lines, then tan theta = (sqrt(2 - 1)) cot prop .

P is a point on either of the two lines y - sqrt3|x|=2 at a distance 5 units from their point of intersection The coordinates of the foot of the perpendicular from P on the bisector of the angle between them are

If the two equal chords of a circle intersect : (i) inside (ii) on (iii) outside the circle, then show that the line segment joining the point of intersection to the centre of the circle will bisect the angle between the chords.

A point P (2, -1) is equidistant from the points (a,7) and (-3,a). Find a.

Two circles with centres A and B intersect each other at points P and Q. Prove that the centre-line AB bisects the common chord PQ perpendicularly.

In triangle LMN, bisector of interior angles at L and N intersect each other at point A. Prove that : AM bisects angle LMN.

The two regression lines intersect at unique point, then it should be

Two parallel lines l and m are intersected by a transversal p . Show that the quadrilateral formed by the bisectors of interior angles is a rectangle.