Hello,

Look at the picture :

I've drawn the segment bisectors of AB and AC. Any point that is on a segment bisector is at equal distance of the extremes of the segment.

D is the intersection point.

Therefore AD=BD=CD.

There is only one circle passing through 3 given distinct points. So D is the center of the circle.

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Now, consider triangles AED and AFD.

E and F are the midpoints of AB and AC.

Because AB=AC,AE=AF.

Moreover, the two triangles have a common side :AD.

Plus, given the property of bisection, DE is perpendicular to AE and DF is perpendicular to AF. So :

angle DEA=angle DFA=90°

Are the triangles congruent ?