Connect OB and OC....these are radii
We have two right triangles
The radii are congruent and the distance from O to each chord is the same
The radii serve as the hypotenuse in each triangle and the distance from O to each chord is a leg
Therefore, by hypotenuse-leg....these triangles are congruent
So the remaining legs ( B to the "top" perpendicular and C to the same perpendicular ) are equal
By the same reasoning, we can prove that the distances from A to its respective perpendicular and C to the same perpendicular are equal if we connect OA and OC
Thus.....the chords will be equal