`D` and `E` are points on equal sides `A B` and `A C` of an isosceles triangle `A B C` such that `A D=A E` . Prove that `B ,C ,D ,E` are concylic.

D\ a n d\ E are, respectively, the points on equal sides A B\ a n d\ A C of an isosceles triangle A B C such that B ,\ C ,\ E ,\ a n d\ D are concyclic as shown in Figure. If O is the point of intersection of C D\ a n d\ B E , prove that A O is the bisector of line segment D E

If D and E are points on sides A B and A C respectively of a triangle A B C such that D E || B C and B D=C E . Prove that A B C is isosceles.

D and E are points on sides AB and AC respectively of Delta A B C such that a r\ (D B C)\ =\ a r\ (E B C) . Prove that D E||B C .

In A B C ,\ D and E are points on sides A B and A C respectively such that A DxxE C=A ExxD B . Prove that D E B C .

A D and B E are respectively altitudes of an isosceles triangle A B C with A C=B C . Prove that A E=B Ddot

B D\ a n d\ C E are bisectors of /_B\ a n d\ /_C of an isosceles A B C with A B=A C . Prove that B D=C E

In Figure, A B C is a triangle in which A B=A Cdot Point D and E are points on the sides AB and AC respectively such that A D=A Edot Show that the points B , C , E and D are concyclic.

D and E are points on sides AB and AC respectively of DeltaA B C such that a r\ (D B C)\ =\ a r\ (E B C) . Prove that D E\ ||\ B C .

D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that A E^2+B D^2=A B^2+D E^2 .

D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that A E^2+B D^2=A B^2+D E^2 .