In order for two triangles to be congruent, they need to have two equal angles. Because AC and BD are diameters, angle A and angle D are equal and both are acute (90 deg). This happens because every angle which faces diameter is acute. So now we have proved that these triangles have 1 identical angle, and we need to prove the same for some another angle. If we take a look to OB and OC, we notice that they are radiuses and have equal sizes, so the angleOBA=angleOCD. Proved.
