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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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Use ruler and compasses only for the following questions:
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