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

If A,B,C are points (-1,1),(1,3) and (3,a) respectively and if AB=Bc, then find 'a'.

ABC is triangle. D is the middle point of BC. If AD is perendicular to AC, then prove that cosAcosC=(2(c^(2)-a^(2)))/(3ac)

If A, B, and C are three square matrices of the same order, then AB=AC implies B=C . Then

ABC is right - angled triangle at B. Let D and E be any two point on AB and BC respectively . Prove that AE^2 + CD^2 = AC^2 + DE^2

The straight lines 3x + 4y =5 and 4x-3y = 15 interrect at a point A(3,-1) . On these linepoints B and C are chosen so that AB = AC . Find the possible eqns of the line BC pathrough the point (1, 2)

In the figure, ABC is a triangle in which AB= AC. Points D and E are points on the side AB and AC respectively such that AD=AE. Show that points B, C, E and D lie on a same circle.

In a right angled DeltaABC,angleACB=90^(@). A circle is inscribed in the triangle with radius r, a, b, c are the lengths of the sides BC, AC and AB respectively. Prove that 2r=a+b-c.

In the adjoining figure, O is the centre and seg AB is a diameter. At point C on the circle, the tangent CD is drawn. Line BD is tangent at B . Prove that seg OD || seg AC.

In the adjoining figure, seg BD bot "side" AC, C-D-A. "Prove that" : AB^(2) = BC^(2) + AC^(2) - BC.AC

If A(-1,1) , B(1,3) and C(3,a) are points and if AB = BC , then