Theory question 104
ConstructionsUsing a ruler and a pair of compasses only, construct a triangle ABC, given that |AB| = 8.4cm, |BC| = 6.5cm and ∠ABC = 30°. Construct the locus: (a) l1 of points equidistant from AB and BC, and within the angle ABC (b) l2 of points equidistant from B and C. Locate the point of intersection P of l1 and l2, measure |AP|.
Show the model answer
Model answer
Draw BC = 6.5 cm. At B construct 60° and bisect it to get 30°; mark A on that arm with BA = 8.4 cm; join AC.
(a) l1 = bisector of ∠ABC (arcs from B, then equal arcs from the cut points).
(b) l2 = perpendicular bisector of BC.
Mark P where l1 and l2 meet.
|AP| ≈ 5.2 cm.
Explanation
Leave all construction arcs visible.