The chords AB and CD of a circle with centre O are equal…

Step 1. The equal sides.

1. $OA = OC$ and $OB = OD$, because they are radii.
2. $AB = CD$, given.

Step 2. The rule. $\triangle AOB \cong \triangle COD$ by SSS. So $\angle COD = \angle AOB = 64^\circ$ by CPCT.

Step 3. The base angle. $OC = OD$, so $\angle OCD = \dfrac{180^\circ - 64^\circ}{2} = 58^\circ$.