Theory question 111
ConstructionsUsing a ruler and a pair of compasses only. (a) Construct: (i) a △ABC such that |AB| = 5cm, |AC| = 7.5cm and ∠CAB = 120°. (ii) the locus l1 of points equidistant from A and B. (iii) the locus l2 of points equidistant from |AB| and AC, which passes through triangle ABC. (b) Label the point P where l1 and l2 intersect. (c) Measure |CP|.
Show the model answer
(a)(i) Draw AB = 5 cm. At A construct 120° (two 60° arcs), mark C on that arm with AC = 7.5 cm, join BC.
(ii) l1 is the perpendicular bisector of AB (arcs from A and B above and below, join the crossings).
(iii) l2 is the bisector of ∠CAB (makes 60° with AB).
(b) Mark P where the two loci meet.
(c) |CP| ≈ 6.6 cm (accept about 6.5–6.8 cm).
Construction arcs must be left visible; the equidistant-from-two-lines locus is an angle bisector.