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

In the given figure, if AC = BD, then prove that AB = CD.

D is a point on side BC ΔABC such that AD = AC (see figure). Show that AB > AD.

In DeltaABC,if AC=8, BC=7 and D lies between A and B such that AD=2, BD=4, then the length CD equals

In an equilateral ABC, E is a point on BC such that BE= (1)/(4)BC . Prove that 16AE^(2)= 13AB^(2) .

If A, B and C are three points on a line, and B lies between A and C (see figure), then prove that AB + BC = AC.

Two circles intersect at two points A and B AD and AC are diameters to the two circles Prove that B lies on the line segment DC.

D is a point on side BC of triangle ABC such that AD = AC (see the given figure). Show that AB gt AD.

In equilateral DeltaABC, D is a point on BC such that BD= (1)/(3)BC . Prove that 9AD^(2)= 7AB^(2) .

ABC is a triangle with AB= AC and D is a point on AC such that BC^(2)= AC xx CD . Prove that BD= BC.

In triangle ABC, D is the midpoint of BC. DFZAB and DE bot AC, where points F and E lie on AB and AC respectively. If DF = DE, prove that A ABC is an isosceles triangle.