• # question_answer Draw a circle with centre C and radius 3.4 cm. Draw any chord$\overline{AB}$. Construct the perpendicular bisector of $\overline{AB}$ and examine if it passes through C.

 To construct the perpendicular bisector of chord $\overline{AB}$. we use the following steps: Step I: Draw a circle with C as centre and radius 3.4 cm. Step II: Now, draw a chord AB of the circle (a chord of a circle is a line segment joining any two points on the circle) Step III: With A as centre, using compasses draw an arc (here, we can draw circle also) with radius more than half of the length of $\overline{AB}$. Step IV: With the same radius and with B as centre, draw an another arc using compasses. Let it cut the previous arc at P and C. Step V: Join $\overline{PC}$ and produce up to Q. It cuts $\overline{AB}$ at O. Therefore, $\overline{PC}$ is the perpendicular bisector of $\overline{AB}$. Also, the perpendicular bisector $\overline{PB}$ passes through the centre C of the circle. Hence, the perpendicular bisector of chord AB passes through the centre C.