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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?
Solution
Steps of construction:
(i) Draw a circle with centre O of radius 6 cm.
(ii) Now, draw a diameter AB of the circle.
(iii) With the centre B and the radius more than `1/2(hat(AB))`, draw the arcs on each side of AB.
(iv) With the centre A and the same radius, draw the arcs on each side of AB which cuts the previously drawn arc at X and Y.
(v) Now join OX and OY and produce them to any points P and Q.
Thus PQ bisects the diameter of a circle. Yes, the perpendicular PQ contains another diameter of this circle.
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