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

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

In triangle ABC , sides AB and AC are extended to D and E, respectively, such that AB=BD and AC =CE , Find DE, if BC=6 cm .

If the equal sides AB and AC (each equal to 5 units) of a right-angled isosceles triangle ABC are produced to P and Q such that BP cdot CQ = AB^(2) , then the line PQ always passes through the fixed point (where A is the origin and AB, AC lie along the positive x and positive y - axis respectively)

ABC is a triangle in which AB=AC.D and E are points on the sides AB and AC respectively,such that AD=AE .Show that the points ' B

In the adjoining figure, ABC is an isosceles triangle in which AB = AC. If E and F be the midpoints of AC and AB respectively, then

In the given figure, /_\ ABC is an isosceles triangle in which AB - AC. If AB and AC are produced to D and E respectively such that BD = CE, prove that BE = CD. Hint. Show that /_\ ACD = /_\ ABE .

In an isosceles triangle ABC with AB=AC a circle passing through B and C intersects the sides AB and AC at D and E respectively. Prove that DE|CB.

In an isosceles triangle ABC with AB=AC , a circle passing through B and C intersects the sides AB and AC at D and E respectively.Prove that DEBC

ABC is an isosceles triangle in which AB=AC. If D and E are the mid-points of AB and AC respectively,prove that the points B,C,D and E are concylic.

ABC is an isosceles triangle in which AB=AC. If D and E are the mid-points of AB and AC respectively,prove that the points B,C,D and E are concyclic.