And you'd have a mayonnaise like goo on the bottom of the oil cap, and might be blowing lots of white smoke out the tailpipe.
All three of these things though, can happen in an engine that gets water in the oil through condensation too, and I've had a dealer try to tell me these were signs of a blown head gasket, when it turned out to be a bad radiator, and a vehicle only driven on short around-town trips (which don't get the oil hot enough to boil off the water).
Coolant leaks can be tricky. You may have more than one (very common). Often, the system only leaks under pressure, so if you fix one leak, the pressure goes higher, and new leaks appear.
I'd get a radiator pressure test kit. They run about $80+. It replaces your radiator cap, when the engine is off and cold. You use a small included pump, to raise the pressure up to operating pressure (this can vary depending on the vehicle), and that may make the leak appear. Pump it too high, and you can damage things.
Check the easy things first. Heater hoses, radiator hoses, thermostat gasket, and radiator end caps. After that, there's the heater core ($$), head gasket ($$$), and radiator ($-$$).
