Question 2
(2) (a) The sides of a triangle PQR are: PQ = 60, QR = 75 and PR (the base) = 100.
(i) Draw, twice full size, the triangle.
(ii) Construct a rectangle equal in area to the triangle.
(iii) Draw and state the length of the diagonal of the rectangle.
(b) Two circles, ∅60 and ∅90, have a centre distance of 150.
(i) Draw the given circles.
(ii) Construct an internal tangent to the two circles.
(iii) State the distance between the points of tangency.
Observation
Candidates’ responses to (a)(i) and (b) were adequate. A few candidates, however, could not adequately answer questions (a)(ii) and (a)(iii). The solutions to the poorly answered questions are given below.
(a) (ii) STEPS INVOLVED IN DRAWING THE TRIANGLE, CONSTRUCTING THE RECTANGLE AND DRAWING THE DIAGONAL OF THE RECTANGLE
Drawing the triangle PQR twice full size
Dropping the perpendicular from the apex Q to locate point M on line P
Bisecting the altitude QM and extending it at both ends
Erecting perpendicular at points P and R to intercept the bisector at points T and S respectively
Completing the rectangle PRST
Stating the length of the diagonal PS = 205mm
(iii) MAJOR STEPS IN DRAWING TRUE SHAPE OF THE CUT SURFACE
Projecting perpendicular lines from points a1, b1 and c1 on the cutting plane
Drawing a reference line X2 Y2 parallel to the cutting plane Y-Y
Transferring corresponding vertical ordinates of the cut surface from X1 Y1on plan to X2 Y2
Joining the points (a3, b3 and c3) to draw the true shape
Sectioning