Let ABC be a given isosceles triangle with AB=AC. Sides AB and AC are extended up to E and F, repectively, such that `BE xx CF = AB^(2)` . Prove that the line EF always passes through a fixed point.

Let A B C be a given isosceles triangle with A B=A C . Sides A Ba n dA C are extended up to Ea n dF , respectively, such that B ExC F=A B^2dot Prove that the line E F always passes through a fixed point.

If Delta ABC is an isosceles triangle with angle C=90^(@) and AC=5 cm, then AB is

In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD (see figure) Show that AD = AE

If Delta ABC is an isosceles triangle with hat(C ) = 90^(@) and AC = sqrt(8) cm then AB is :

In a triangle ABC, if D and E are mid points of sides AB and AC respectively. Show that vecBE+ vecDC=(3)/(2)vecBC .

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

ABC is an isosceles triangle right angled at C. Prove that AB^(2) = 2AC^(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.