It is known that in the triangle ABC the smallest side is BC. Let X,Y,K and L - points on the sides AB,AC and on the rays CB,BC, respectively, are such that BX=BK=BC=CY=CL. The line KX intersects the line LY at the point M. Prove that the intersection point of the medians △KLM coincides with the center of the inscribed circle △ABC. geometryincenterCentroidequal segments