WAEC 2009 · Paper 2 · Q10

(a)
Using a ruler and a pair of compasses only, construct a triangle $ABC$ such that $|AB| = 7.1$ cm, $|AC| = 7$ cm and $\angle BAC = 105^\circ$ . Construct the bisector of $\angle BAC$ to meet $BC$ at $X$ , and the perpendicular bisector of $AC$ to meet $AX$ produced at $Y$ .
Model answer
Construct $105^\circ$ at $A$ as $90^\circ + 15^\circ$ (bisect the $30^\circ$ between $90^\circ$ and $120^\circ$ ). Mark $B$ and $C$ , join $BC$ . Bisect angle $BAC$ and extend the bisector beyond $BC$ . Construct the perpendicular bisector of $AC$ ; where it meets $AX$ produced is $Y$ . Leave all arcs visible.
(b)
Measure: (i) $|XY|$ ; (ii) $|BC|$ .
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

Draw $AB = 7.1$ cm.
At $A$ construct $90^\circ$ , then $120^\circ$ , and bisect the angle between them to get $105^\circ$ .
Mark $C$ on this arm with $AC = 7$ cm and join $BC$ .
Bisect angle $BAC$ .
The bisector meets $BC$ at $X$ .
Extend it beyond $X$ .
Construct the perpendicular bisector of $AC$ .
It meets $AX$ produced at $Y$ .