(1) So simple! Minor TU is 180 - 32 = 148 degrees.

(2) I will have to think about this one...

(3) The external tangent gives us similar triangles OTC and PUC. Let x = PC. Then x/(x + 5) = 3/8, so x = 3. The answer is PC = 3 + 3 + 5 = 11.