Solution:

Take the midpoint m of AB and connect OM and CM.

Yi Yi OM= 1/2AB= 1, CM=√5 (obtained by Pythagorean theorem).

According to the fact that the sum of two sides of a triangle is greater than the third side, we can know that OC≤OM+CM.

Only when the line * * * of O, M and C holds.

The maximum value of ∴OC is ∴ 5+ 1.