BG-MO 1985 Problem 3

A pyramid $MABCD$ with the top-vertex $M$ is circumscribed about a sphere with center $O$ so that $O$ lies on the altitude of the pyramid. Each of the planes $ACM,BDM,ABO$ divides the lateral surface of the pyramid into two parts of equal areas. The areas of the sections of the planes $ACM$ and $ABO$ inside the pyramid are in ratio $(\sqrt2+2):4$ . Determine the angle $\delta$ between the planes $ACM$ and $ABO$ , and the dihedral angle of the pyramid at the edge $AB$ .