1st Irish Mathematical Olympiad Problems 1988

1.  One face of a pyramid with square base and all edges 2 is glued to a face of a regular tetrahedron with edge length 2 to form a polyhedron. What is the total edge length of the polyhedron? 2.  P is a point on the circumcircle of the square ABCD between C and D. Show that PA2 - PB2 = PB·PD - PA·PC.