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in Class X Maths by (-12,632 points)

Ruler and compasses only may be used in this question. All construction 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 centre A and radius 2.5 cm. Let it meet AB at D.

(iii) Construct a circle to touch the circle with centre A externally at D and also to touch the line BC.

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Steps of construction :

(i) Take BC = 20 cm.

(ii) Make ABC = 45˚ and with centre B, cut the arc BA = 9 cm.

(iii) Join AC, so ABC is the required triangle.

(iv) With A as centre and radius = 25 cm, draw a circle. It will pass through D.

(v) Draw DE and AB, which  cuts BC at E.

(vi) Draw the angle bisector of BED which cut BD at O.

(vii) Taking radius  = OD draw a circle which touches the first circle at D and also touches the line BC at F.

(viii) This is the required circle. The radius OD = 2.7 cm 

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