If A,B,C are three points on a line and B lies between A and C, then prove that AC-AB = BC

Prove that A(BC)=(AB)C

If a point C lies between two points A and B, such that AC=BC , then prove that AC=1/2 AB . Explain by drawing the figure.

If a point 'C' lies between two points A and B such that AC =BC , then prove that AC=1/2 AB . Explain by drawing the figure.

In Delta ABC , /_ B = /_C , D and E are the points on AB and AC such that BD = CE , prove that DE || BC .

If the position vectors of the points A,B and C be a,b and 3a-2b respectively, then prove that the points A,B and C are collinear.

If A, B, C and D aare four points and vec AB = vec DC then vec AC + vec BD =

D and E are points on sides AB and AC respectively of tirangle ABC such that ar (DBC) = ar (EBC) . Prove that DE || BC

Let ABC be a triangle and D and E be two points on sides AB such that AD = BE . If DP || BC and EQ || AC , then prove that PQ || AB .

In Fig A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR . Show that BC || QR.

There are five points A,B,C,D and E. no three points are collinear and no four are concyclic. If the line AB intersects of the circles drawn through the five points. The number of points of intersection on the line apart from A and B is