Use ruler and compass for this question :
(a) Draw line segment AB of length 6 cm.
(b) Construct the locus of points which are equidistant from A and B. Mark a point on the locus which is 4.5 cm from A. Name this point as O.
(c) Construct the locus of all points which are 4.5 cm from O.
(d) Mark the point of intersection of loci (b) and (c) as P, which is on the same side of AB as O.
(e) Construct the locus of points which are equidistant from AP and AB.
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Steps of construction :
Draw a line segment AB of length 6 cm.
Draw XY, the perpendicular bisector of AB. XY is the locus of points which are equidistant from A and B.
With A as centre and radius 4.5 cm, draw an arc cutting XY at the point O. Thus, O is the point on the locus which is 4.5 cm from A.
With O as centre and radius 4.5 cm, draw a circle. This circle is the locus of all points which are 4.5 cm from O.
Mark P, the point of intersection of the perpendicular bisector XY and the circle, which lies on the same side of AB as O.
Join AP.
Draw AZ, the bisector of ∠PAB. AZ is the locus of points which are equidistant from AP and AB.
