Theory question 109
Constructions(a) Using a ruler and a pair of compasses only, construct: (i) a triangle PQR such that |PQ| = 10 cm, |QR| = 7 cm and PQ̂R = 90°; (ii) the locus l1 of points equidistant from Q and R; (iii) the locus l2 of points equidistant from P and Q.
(b) Locate the point O equidistant from P, Q and R.
(c) With O as centre, draw the circumcircle of the triangle PQR.
(d) Measure the radius of the circumcircle.
Show the model answer
(a)(i) Draw PQ = 10 cm, construct 90° at Q and mark QR = 7 cm; join PR.
(ii) l1 is the perpendicular bisector of QR. (iii) l2 is the perpendicular bisector of PQ.
(b) O is where l1 and l2 meet (it is the midpoint of PR).
(c) Circle with centre O through P, Q and R.
(d) Radius ≈ 6.1 cm (half of PR = ½√149 ≈ 6.10 cm).
Points equidistant from two points lie on their perpendicular bisector.