Question

D is a point on the circumcircle of `Delta ABC` in which `AB=AC` such that `B` and `D` are on opposite sides of line AC. If CD is proudced to a point E such that `CE=BD`, prove that `AD=AE`.

Answer 1

In `Delta ABD` and `DeltaACE`, we have
`AB=AC`(given)
`BD=CE` (given)
`therefore angle 1 =angle 2` (angles in same segment )
`rArrDeltaABDcongDeltaACE` (SAS congruency)
`rArrAD=AE`(c.p.c.t).