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I have a doubt in constructing a perpendicular bisector.Now,how do we construct a perpendicular bisector if there is a fixed length say AB=7cm? 

Take AB = 7cm and follow the steps given in the following link :

 

https://www.meritnation.com/ask-answer/question/can-we-draw-a-perpendicular-bisector-without-drawing-a-circ/practical-geometry/1671030

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first take point a as the centre with the compass and make two arcs - one above and one below with the radius of more than half of ab.then take b as the centre and with the same radius  draw two more arcs intersecting the previous arcs      c and d. then  draw a line through c and which gives the perpendivcular bisector of ab = 3.5 cm

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