`B D` and `C E` are bisectors of `/_B` and `/_C` of an isosceles ` A B C` with `A B=A Cdot` Prove that `B D=C Edot`

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 D\ a n d\ B E are respectively altitudes of an isosceles triangle A B C with A C=B Cdot Prove that A E=B D

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

In an isosceles triangle A B C with A B=A C and B D_|_A Cdot Prove that B D^2-C D^2=2C DdotA Ddot

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.

In Figure, A B=A C\ a n d\ D B=D Cdot\ Prove that /_A B D=/_A C D

In Figure, if A B=A C\ a n d\ B E=C D , prove that A D=A Edot

In Figure A B D C\ a n d\ A D B Cdot Prove that /_D A B=\ /_D C B

The bisector of /_B of an isosceles triangle A B C with A B=A C meets the circumcircle of A B C at P as shown in Figure. If A P\ a n d\ B C produced meet at Q , prove that C Q=C A .

The bisector of interior /_A of A B C meets B C in D , and the bisector of exterior /_A meets B C produced in Edot Prove that (B D)/(B E)=(C D)/(C E)dot