6th Mexican Mathematical Olympiad Problems 1992

6th Mexican Mathematical Olympiad Problems 1992A1.  The tetrahedron OPQR has the ∠POQ = ∠POR = ∠QOR = 90o. X, Y, Z are the midpoints of PQ, QR and RP. Show that the four faces of the tetrahedron OXYZ have equal area. A2.  Given a prime number p, how many 4-tuples (a, b, c, d) of positive integers with 0 < a, b, c, d < p-1 satisfy ad = bc mod p?