We know, that tangents drawn from an external point are equal.

AD = AF

[tangents from point A] [1]

BD = BE

[tangents from point B] [2]

CF = CE

[tangents from point C] [3]

Now,

AB = AC [Given] …[4]

Substracting [1] From [4]

AB - AD = AC - AF

BD = CF

BE = CE [From 2 and 3]

Hence Proved.