Theory question 110
Constructions(a) Using ruler and a pair of compasses only, construct: (i) a quadrilateral PQRS such that |PQ| = 7 cm, ∠QPS = 60°, |PS| = 6.5 cm, ∠PQR = 135° and |QS| = |QR|; (ii) locus l1 of points equidistant from P and Q; (iii) locus l2 of points equidistant from P and S.
(b)(i) Label the point T where l1 and l2 intersect. (ii) With centre T and radius |TP|, construct a circle l3.
Show the model answer
(a)(i) Draw PQ = 7 cm; construct 60° at P and mark PS = 6.5 cm. Construct 135° at Q (90° + 45°). With centre Q and radius QS, cut the 135° arm at R. Join SR.
(ii) l1: perpendicular bisector of PQ. (iii) l2: perpendicular bisector of PS.
(b)(i) T is where l1 and l2 meet.
(ii) The circle centre T, radius TP, passes through P, Q and S (radius ≈ 3.9 cm).
T is equidistant from P, Q and S, so the circle passes through all three.