Question

Draw a circle of radius $4cm.$ Draw any two of its chords. Construct the perpendicular bisectors of these chords. Where do they meet?

Answer 1

A perpendicular bisector of a line segment is a line perpendicular to and passing through the midpoint of the line segment.

Steps of construction:

(i) Draw the circle with $O$ as center and radius $4cm.$

(ii) Draw any two chords $\overline{AB}$ and $\overline{CD}$in this circle.

(iii) Taking $A$ and $B$ as centers and radius more than half $AB,$ draw two arcs that intersect each other at $E$ and $F.$

(iv) Join $EF.$ Thus $EF$ is the perpendicular bisector of chord $\overline{AB}$.

(v) Similarly, draw $GH$ the perpendicular bisector of chord $\overline{CD}$

(vi) These two perpendicular bisectors meet at $O,$ the center of the circle.