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Let the circle you draw side on AB of triangle ABC intersects the base BC at a point E and the center of the circle you draw be O. then
so triangle OBE is isosceles and angle OBE = angle ABC
therefore triangles ABC and OBE are similar.(if two isosceles triangles have same base angle they are similar) 
then (OB/AB) =(BE/BC)
but (OB/AB)=1/2
therefore (BE/BC)=1/2
therefore E divides BC into two
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