Using a ruler and compass only, construct:
(a) ∆ABC such that AB = 5 cm, AC = 6.3 cm and ∠ABC = 60°.
(b) the circumcircle of ∆ABC.
(c) the locus of points which are equidistant from AB and BC.
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(a) Steps of construction :
Draw a line segment AB = 5 cm.
At B, construct ∠ABX = 60°.
With A as centre and radius 6.3 cm, draw an arc cutting the ray BX at C.
Join AC. Thus, ∆ABC is constructed.
In ∆ABC, draw the perpendicular bisectors of any two sides (say AC and BC). Let them intersect at O.
With O as centre and radius OA, draw a circle. This is the circumcircle of ∆ABC passing through A, B and C.
In ∆ABC, draw the bisector of ∠ABC. This bisector is the locus of points equidistant from AB and BC.
Hence, the required construction is completed, where the bisector of ∠ABC is the locus of points equidistant from AB and BC.