So triangle SOQ is all equal to triangle TOP.
So angle OSC= angle OTC
And because angle PCS= angle QCT.
PS=QT(OS-OP=OT-OQ)
So triangle PCS is all equal to triangle QCT.
So PC=QC
And oc = oc and op = OQ.
So triangle OPC is all equal to triangle OQC.
So ∠OPC=∠OQC
That is, OC bisects ∠AOB