`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`

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

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

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 a triangle A B C , the internal bisectors of /_B\ a n d\ /_C meet at P and the external bisectors of /_B\ a n d\ /_C meet at Q . Prove that /_B P C+\ /_B Q C=180^0

In a quadrilateral A B C D ,\ C O\ a n d\ D O are the bisectors of /_C\ a n d\ /_D respectively. Prove that /_C O D=1/2(/_A+/_B)dot

In a quadrilateral A B C D ,\ C O\ a n d\ D O are the bisectors of /_C\ a n d\ /_D respectively. Prove that /_C O D=1/2(/_A+/_B)dot

In Figure, A E bisects /_C A D\ a n d\ /_B=/_Cdot Prove that A E||B C

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

A D\ a n d\ B E are respectively altitudes of A B C such that A E=B D . Prove that A D=B E .