`D` is a point on the circumcircle of ` A B C` in which `A B=A C` such that `B\ a n d\ D` are on the opposite side of line `A Cdot` If `C D` is produced to a point `E` such that `C E=B D ,` prove that `A D=A E`

Explanation

Given that `D` is a point on the circumcircle triangle `ABC` in which `AB=AC` such that `B` and `D` are on the opposite side of the line `AC` Also if `CD` is produced to a point E such that `CE = BD` then. we have to find which is equal to `AD`.We join `A` and `E`
We know that angles in same segment of circle are equal.
SO` /_ABD = /_ACD`
because the angle is in same segment `AD`
Now given that `AB = AC`and `CE=BD`(congruent)
Therefore
`/_\ ABD ~= /_\AEC` by `SAS` Rule.
`SAS` side, stands for "side, angle, side"are equal to For any two triangles if two sides and the included angle af one triangle the corresponding sides and angle af anothers triangle, then two triangles are.. congruent
Therefore `AD = AE`