If a line segment joining two points subtends equal angles at two other points lying on the same side of the line segment; the four points are concyclic.

Theorem: 7 If the line segment joining two points subtends equal angles at two other points lying on the same side of the line segment; the four points are concyclic.i.e lie on the same circle.

If the segment joining the points (a,b),(c,d) subtends a right angle at the origin,then

Mid point of a line Segment

If the line segment joining the points A(a,b) and B(c,d) subtends an angle theta at the origin, then costheta is equal to

Direction ratio of the line segment joining two points

Find the midpoint of the line segment joined the two points (2,3) and (4,1).

(ii) No two line segments with a common end points are coincident.

Interior point of a line segment

If the line segment joining the points A(a,b) and B (c, d) subtends a right angle at the origin, show that ac+bd=0

Two line segments may intersect at two points