Draw a circle with centre C and radius 4.2 cm. Draw any chord AB. Construct the perpendicular bisector of AB and examine if it passes through C.

Steps:

1. Mark a point C on the sheet of paper.

2. With C as centre and radius 4.2 cm, draw a circle.

3. Mark any two points A and B on the circle and join them. $\overline{AB}$ is a chord of the circle.

4. With A as centre and any suitable radius $\left(\gt\dfrac{1}{2}\text{AB}\right)$, draw arcs on each side of AB.

5. With B as centre and the same radius, draw arcs on each side of AB to cut the previous arcs at P and Q.

6. Draw a line passing through points P and Q.

On examining, we find that the perpendicular bisector PQ of chord $\overline{AB}$ passes through the centre C of the circle.

Hence, yes, the perpendicular bisector of $\overline{AB}$ passes through C.