Let ABC be an acute triangle. Construct a point X on the different side of C with respect to the line AB and construct a point Y on the different side of B with respect to the line AC such that BX=AC, CY=AB, and AX=AY. Let A′ be the reflection of A across the perpendicular bisector of BC. Suppose that X and Y lie on different sides of the line AA′, prove that points A, A′, X, and Y lie on a circle. geometrycongruent triangles