Question

# 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?

A

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

B

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

C

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

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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