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Question

Ali was asked to construct a square for which, the diagonal alone is given (length known) and nothing else. He was given a compass and a straight edge (a ruler with NO markings). The square is ACBD. 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?

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Solution

The correct option is **B**

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

Steps of Construction:

Take the line segment of length AB (the diagonal) and draw the perpendicular bisector of this segment. Let this perpendicular cut AB at P.

With P as the centre and radius AP, cut arcs C and D on the perpendicular bisector. Join AC and AD, BC and BD. We have the square.

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