Car overheated twice in one week, broken.

Car overheated twice in one week, broken pully tore the belt, then a small return hose to resevoir broke. Car was driven 10 miles with broken belt, and 4 miles the second episode.
Coolant is lost with no visible signs. No white smoke from exhause, Engine runs almost perfect with very minor "shake" till it warms up . Then perfect. Where is it going. If head gasket problem, why no smoke, How do I test for head gasket.