Let me see if I get this straight. You want to find maxT while C's are always greater than T?

Then it must be maxT=min{C1,C2} for X1,X2. If your X's are defined throught the plane, just solve

and compare the values to see which ones yield the minima. The min of these is maxT.

If though your variables belong in some region, then use Lagrange coefficients.