Point S is the midpoint of arc ACB of the circumscribed circle k around triangle ABC with AC>BC. Let I be the incenter of triangle ABC. Line SI intersects k again at point T. Let D be the reflection of I across T and M be the midpoint of side AB. Line IM intersects the line through D, parallel to AB, at point E. Prove that AE=BD. geometryincentergeometric transformationreflection