Theory question 110
ConstructionsThe sketch shows a plot of land (|AB| = 85 m, ∠CAB = 40°, ∠ABC = 95°). (a) Using a scale of 1 cm to 10 m draw an accurate diagram of the plot. (b) Construct: (i) the locus l1 of points equidistant from AC and BC (ii) the locus l2 of points 60 m from A. (c) A tree T inside the plot, is on both l1 and l2. Locate T and find |TC| in metres. (d) A flag pole, P is to be placed such that it is nearer AC than BC and more than 60 m from A. Shade the region where P can be located.
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(a) Draw AB = 8.5 cm, angle 40° at A and 95° at B; the arms meet at C (AC ≈ 12.0 cm, BC ≈ 7.7 cm, ∠C = 45°).
(b)(i) l1: bisector of ∠ACB.
(ii) l2: arc of a circle centre A, radius 6 cm.
(c) T is where the bisector meets the arc inside the plot; TC ≈ 7.2 cm on the drawing, i.e. about 72 m.
(d) Shade the part of the plot on the AC side of the bisector of ∠C and outside the arc of radius 6 cm about A.
Equidistant from two lines: angle bisector. A fixed distance from a point: circle.