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Question
Use ruler and compasses only for this question:
I. Construct ABC, where AB = 3.5 cm, BC = 6 cm and ABC = 60o.
II. Construct the locus of points inside the triangle which are equidistant from BA and BC.
III. Construct the locus of points inside the triangle which are equidistant from B and C.
IV. Mark the point P which is equidistant from AB, BC and also equidistant from B and C. Measure and records the length of PB.
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Solution
Steps of constructions:
1) Draw a line BC = 6 cm and CBX = 60°. Cut off AB = 3.5 cm. Join AC, ΔABC is the required triangle.
2) Draw perpendicular bisector of BC and bisector of ∠B.
3) The bisector of ∠B meets bisector of BC at P, therefore BP is the required length,
Where BP = 3.5 cm
4) P is the point which is equidistant from BA and BC, also equidistant from B and C.
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Ruler and compasses only may be used in this question. All construction lines and arcs must be clearly shown, and be of sufficient length and clarity to permit assessment.
(i) Construct a ΔABC, in which BC = 6 cm, AB = 9 cm and ∠ABC = 60°.
(ii) Construct the locus of the vertices of the triangles with BC as base, which are equal in area to ΔABC.
(iii) Mark the point Q, in your construction, which would make ΔQBC equal in area to ΔABC, and isosceles.
(iv) Measure and record the length of CQ.
