Given an acute isosceles triangle ABC,AK and CN are its angle bisectors, I is their intersection point . Let point X be the other intersection point of the circles circumscribed around △ABC and △KBN. Let M be the midpoint of AC. Prove that the Euler line of △ABC is perpendicular to the line BI if and only if the points X,I and M lie on the same line. (Kivva Bogdan) geometryEuler Lineincentercollinearperpendicularisosceles