Question

i. 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. 

ii. Taking any other point Q on the line l, if a circle is drawn with centre Q and radius QA, will it pass through B? Think. 

iii. How many such circles can be drawn, passing through A and B? Where will their centres lie?

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)