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Question
Use ruler and compass only for the following question. All construction lines and arcs must be clearly shown.
- Construct a ΔABC in which BC = 6.5 cm, ∠ABC = 60°, AB = 5 cm.
- Construct the locus of points at a distance of 3.5 cm from A.
- Construct the locus of points equidistant from AC and BC.
- Mark 2 points X and Y which are at a distance of 3.5 cm from A and also equidistant from AC and BC. Measure XY.
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Solution
- Steps of construction:
- Draw BC = 6.5 cm using a ruler.
- With B as center and radius equal to approximately half of BC, draw an arc that cuts the segment BC at Q.
- With Q as center and same radius, cut the previous arc at P.
- Join BP and extend it.
- With B as center and radius 5 cm, draw an arc that cuts the arm PB to obtain point A.
- Join AC to obtain ΔABC.
- With A as center and radius 3.5 cm, draw a circle.
The circumference of a circle is the required locus.
- Draw CH, which is bisector of ΔACB. CH is the required locus.
- Circle with center A and line CH meet at points X and Y as shown in the figure. xy = 5 cm (approximately).
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Ruler and compass 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 Δ ABC, in which BC = 8 cm, AB = 5 cm, ∠ ABC = 60°.
(ii) Construct the locus of point 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 as P, the point which is equidistant from AB, BC and also equidistant from B and C.
(v) Measure and record the length of PB.
