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Ali was asked to construct a square for which only the length of the diagonal alone is given. He was given a compass and a straight edge (a ruler with NO markings). The square is ACBD with AB as one of its diagonal. P is said to be the point of intersection of the diagonals of the square.
Which of the following is constructed as a first step in this construction?



Your Answer
A

B or CD, P, AP or PB or OC or OD

Correct Answer
B

AC or CD, P, AP or PB or OC or OD

Your Answer
C

AB or BD, P, AP or PB or OC or OD

Your Answer
D

AD or CD, P, AP or PB or OC or OD


Solution

The correct option is C

AC or CD, P, AP or PB or OC or OD


Steps of Construction:

1. Take the line segment of length AB (the diagonal) and draw the perpendicular bisector of this segment.

2. Let this perpendicular cut AB at P. With P as the centre and radius AP, cut arcs C and D on the perpendicular bisector.

3. Join AC and AD, BC and BD. We have the square.

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