Use ruler and compass only for the following question. All constr… - Vidyadip

Question

Use ruler and compass only for the following question. All construction lines and arcs must be clearly shown.

(i) Construct a ΔABC in which BC = 6.5 cm, ∠ABC = 60°, AB = 5 cm.

(ii) Construct the locus of points at a distance of 3.5 cm from A.

(iii.) Construct the locus of points equidistant from AC and BC.

(iv)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.

✓

Answer

i. Steps of construction:
1. Draw BC = 6.5 cm using a ruler.
2. With B as center and radius equal to approximately half of BC, draw an arc that cuts the segment BC at Q.
3. With Q as center and same radius, cut the previous arc at P.
4. Join BP and extend it.
5. With B as center and radius 5 cm, draw an arc that cuts the arm PB to obtain point A.
6. Join AC to obtain ΔABC.

ii. With A as center and radius 3.5 cm, draw a circle.
The circumference of a circle is the required locus.

iii. Draw CH, which is bisector of Δ ACB. CH is the required locus.

iv. Circle with center A and line CH meet at points X and Y as shown in the figure. xy = 8.2 cm (approximately)

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