Question

Draw a circle of radius 6 cm using ruler and compasses. Draw one of its diameters. Draw the perpendicular bisector of this diameter. Does this perpendicular bisector contain another diameter of the circle?

Answer 1

Construct a circle of radius 6 cm :

• Mark a point O. ( For centre)
• Set the distance between arms of compass as 6 cm.
• Now, place the pointer of the compass on O and draw a complete circle.
• Mark any point on the circle as A. Thus, OA is the radius of required circle.

• Draw one diameter of circle :
• Extend the line AO so that the line segment intersects circle at B.
• Thus, AB is the required diameter of circle.
• Construct perpendicular bisector to diameter AB.
• Take A and B as centres and draw arcs on both sides of line segment AB with radius more than half of AB.
• Name the points of intersections of arcs above and below the line segment AB as D and E respectively
• Join D and E.

Check if perpendicular bisector contain another diameter of the circle.
From the construction, we can observe that perpendicular bisector DE passes through the centre of the circle.
Thus, perpendicular bisector contains another diameter of the circle.