I can't type mathematical symbols, I can only use words instead. Please forgive me.

(1) Proof: Because OB=OC

So OBC angle = OCB angle.

And because the angle BEC= angle CDB (right angle), BC=CB.

So triangle CDB and triangle BEC are congruent.

So angle DBC= angle ECB

So AB=AC

So triangle ABC is an isosceles triangle

(2) in

The bisector of the proof angle BAC passes through BC to D.

Because AB=AC

So AD divided BC vertically (three lines in one).

Connecting outer diameter

Because d is the midpoint between BC and OB=OC.

So OD vertically divides BC (three lines in one)

And because BC was divided vertically in AD.

So the three-point * * * line of OAD

So o is on the bisector of the angle BAC.