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

AB is a line - segment. P and Q are points on either side of AB such that each of them is equidistant from the points A and B (See Fig ). Show that the line PQ is the perpendicular bisector of AB.

What is the name given to a line intersecting a circle in two points ?

A line intersecting a circle in two points is called a secant .

If P(x, y) is a point equidistant from the points A(6, -1) and B(2, 3), show that x-y = 3.

If the direction ratios of two lines are (5,-12,13) and (-3,4,5) then the angle between them is

Fill in the blanks: If two lines intersect at a point, and if one pair of vertically opposite angels are acute angles, then the other pair of vertically opposite angles are ______.

In a parallelogram OABC vectors a,b,c respectively, THE POSITION VECTORS OF VERTICES A,B,C with reference to O as origin. A point E is taken on the side BC which divides it in the ratio of 2:1 also, the line segment AE intersects the line bisecting the angle angleAOC internally at point P. if CP when extended meets AB in points F, then Q. The position vector of point P is

The direction cosines l, m, n of two lines are connected by the relation l+m+n=0 and l . m=0 then the angle between them is

l and m are two parallel lines intersected by another pair of parallel lines p and q. Show that triangleABC ~= triangleCDA

A secant is a line which intersects the circle at two distinct points and the line segment between the points is a chord.