Question

Activity : Draw segment AB. Draw
perpendicular bisector l of the
segment AB. Take point P on
the line l as centre, PA as radius and draw a circle. Observe that the circle passes through point B also. Find the reason. (Recall
the property of perpendicular
bisector of a segment.)

Taking any other point Q on the line l, if a circle is drawn with centre Q and radius​

Answer 1

i. Draw the circle with centre P and radius PA. line l is the perpendicular bisector of seg AB. Every point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. ∴ PA = PB … [Perpendicular bisector theorem] ∴ PA = PB = radius ∴ The circle with centre P and radius PA passes through point B. ii. The circle with any other point Q and radius QA is drawn. QA = QB = radius … [Perpendicular bisector theorem] ∴ The circle with centre Q and radius QA passes through point B. iii. We can draw infinite number of circles passing through A and B. All their centres will lie on the perpendicular bisector of AB (i.e., line l)Read more on Sarthaks.com - https://www.sarthaks.com/851314/draw-segment-draw-perpendicular-bisector-segment-take-point-the-line-centre-radius-draw