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Question
Construct an isosceles triangle ABC such that AB = 6 cm, BC = AC = 4 cm. Bisect ∠C internally and mark a point P on this bisector such that CP = 5 cm. Find the points Q and R which are 5 cm from P and also 5 cm from the line AB.
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Solution
Steps of construction:
- Draw a line segment AB = 6 cm.
- With centers A and B and radius 4 cm, draw two arcs which intersect each other at C.
- Join CA and CB.
- Draw the angle bisector of angle C and cut off CP = 5 cm.
- A line m is drawn parallel to AB at a distance of 5 cm.
- P as centre and radius 5 cm, draw arcs which intersect the line m at Q and R.
- Join PQ, PR and AQ.
Q and R are the required points.
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(i) a triangle ABC in which AB = 5.5 cm, BC = 3.4 cm and CA = 4.9 cm.
(ii) the locus of point equidistant from A and C.
(iii) a circle touching AB at A and passing through C.
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.
