Theory question 109
ConstructionsUsing ruler and a pair of compasses only, (a) construct a rhombus PQRS of side 7 cm and ∠PQR = 60°; (b) locate point X such that X lies on the locus of points equidistant from PQ and QR and also equidistant from Q and R; (c) Measure |XR|.
Show the model answer
Model answer
(a) Draw QR = 7 cm; construct 60° at Q and mark QP = 7 cm; with centres P and R, radius 7 cm, find S. Join PS and RS.
(b) Bisect ∠PQR (points equidistant from PQ and QR) and draw the perpendicular bisector of QR (points equidistant from Q and R). X is where they meet.
(c) |XR| ≈ 4.0 cm (exactly 3.5/cos 30° ≈ 4.04 cm).
Explanation
The bisector of the angle at Q makes 30° with QR.