Refer to the diagram below. It seems that the properties of ZACM and ZBCX are not clear. Let the two circles intersect at x and Z. There are many right angles in the diagram and hence, a lot of concyclicity. In particular, one sees that the lines DE and FG intersect at Z. (Can you show it?) M Observe the diagram. It seems that Clies on XZ, the common chord (and the radical axis) of the two circles. This is not difficult to show, by calculating the power of C with respect to the two circles, because we have many equal lengths in the diagram due to the squares. It follows that ZBCX = ZCZD (because Clies on xz). One sees that C, D, Z, F are concyclic and hence, ZCZD = ZCFD. It suffices to show that Z ACM = ZCFD, where M is the midpoint of AB. Refer to the diagram below. It is much simpler! Does the diagram look familiar?! Refer to the diagram below. It seems that the properties of ZACM and ZBCX are not clear. Let the two circles intersect at x and Z. There are many right angles in the diagram and hence, a lot of concyclicity. In particular, one sees that the lines DE and FG intersect at Z. (Can you show it?) M Observe the diagram. It seems that Clies on XZ, the common chord (and the radical axis) of the two circles. This is not difficult to show, by calculating the power of C with respect to the two circles, because we have many equal lengths in the diagram due to the squares. It follows that ZBCX = ZCZD (because Clies on xz). One sees that C, D, Z, F are concyclic and hence, ZCZD = ZCFD. It suffices to show that Z ACM = ZCFD, where M is the midpoint of AB. Refer to the diagram below. It is much simpler! Does the diagram look familiar