Question

Ruler and compasses only may be used in this question. All constructions lines and arcs must be clearly shown, and the be sufficient length and clarity to permit assessment:
(i) Construct a triangle ABC, in which AB = 9 cm, BC = 10 cm and angle ABC = 45°.
(ii) Draw a circle, with center A and radius 2.5 cm. Let it meet AB at D.
(iii) Construct a circle to touch the circle with center A externally at D and also to touch the line BC.

Answer 1

Steps of construction:
1) Take BC = 10 cm
2) Make ∠ ABC = 45° and with centre B, cut the arc = 9 cm.
3) Join AC, So Δ ABC is the required triangle.
4) With A as centre and radius = 2.5 cm, draw a circle. It will pass through D.
5) Draw DE ⊥ AB, which cuts BC at E.
6) Draw the angle bisector of ∠ BED which cut BD at O.
7) Taking Radius = OD to draw a circle which touches the first circle at D and also touches the line BC at F.
8) This is the required circle. The radius OD = 2.7 cm.