Question

(i) Construct a triangle ABC, in which AB = 5.0 cm, BC = 3.5 cm and ∠ ABC = `67 1/2°`
( Use a pair of compasses and ruler only.)
(ii) Construct a circle to touch AB at B and it pass though C.

Answer 1

Steps of construction:
1) Draw BC = 3.5 cm.
2) At B draw BE such that ∠ EBC = `67 1/2°`. From BE cut off BA = 5 cm
3) Join AC. Then ΔABC is the required triangle.
4) Produce EB to F.
5) At B draw BG such that ∠ EBG = 90°.
6) Draw perpendicular bisector of BC to cut BG at O.
7) With O as centre and OB as radius draw a circle. This is the required circle to touch AB at B and pass-through C.