Using a ruler and a pair of compasses only, (a) construct (i) a triangle ABC such that |AB| = 5cm, |AC| = 7.5cm and < CAB = 120° ; (ii) the locus \(L_{1}\) ...

Construction

1. Draw the line segment \(AB=5\text{ cm}\).
2. At \(A\), construct an angle of \(120^\circ\). With centre \(A\) and radius \(7.5\text{ cm}\), cut this ray at \(C\). Join \(BC\).
3. With centres \(A\) and \(B\), and with the same compass radius greater than \(2.5\text{ cm}\), draw arcs above and below \(AB\) to intersect. Join the arc-intersection points. This is \(L_1\), the perpendicular bisector of \(AB\).
4. Construct the internal angle bisector of \(\angle BAC\). This is \(L_2\), the locus of points equidistant from the lines \(AB\) and \(AC\).
5. Label the intersection of \(L_1\) and \(L_2\) as \(P\).

Measurement:

Measuring the constructed line gives