Question

Draw a circle of radius 6 cm. Draw its diameter and name it AB. Using compasses and ruler, construct the perpendicular bisector of AB. Does it pass through the center of the circle?

Answer 1

Hint: Perpendicular bisector of any chord of a circle will pass through the center of the circle. The perpendicular bisector of any chord of a circle must pass through the center of that circle where a circle is a shape consisting of all the points that are at equidistant from a given point, and it can also be defined as a closed, two-dimensional curved shape.
In this question it is asked to draw a circle with a radius of 6 cm, hence use a ruler to draw a diameter AB to take it as a base and then use a compass to bisect the diameter to draw a perpendicular bisector.

Complete step by step solution:
Given the radius of the circle 6 cm.
Step 1: Use a ruler and compass and set the compass at 6 cm to draw a circle of radius 6 cm.
Step 2: Now draw a line passing through the center and joining at the endpoint of the circle at both sides, mark it as AB, which will be the diameter of the circle.
Step 3: Now place the compass at one end of line segment AB and adjust the compass slightly more than the half of the line segment and draw an arc above and below the line.
Step 4: Now draw a line PQ joining both the arc above and below of line segment AB.
Hence the line PQ will be our required line which will be the perpendicular bisector of AB.
                                          

Thus PQ bisects the diameter of a circle.
Hence it passes through the center of the circle.

Note: Students should be aware while using different plotting (or measuring) instruments. If any error even in centi-meters is there while plotting then, your sketch could not be considered as appropriate.