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Using a ruler and compasses only :

(i) Construct a triangle ABC with the following data :

AB = 3.5 cm, BC = 6 cm and ∠ABC = 120°.

(ii) In same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.

(iii) Measure ∠BCP.

Constructions

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Answer

Steps of construction :

  1. Draw a line BC = 6 cm.

  2. At B, draw a ray BX making an angle of 120° with BC. With B as center and radius 3.5 cm, cut off AB = 3.5 cm.

  3. Join AC. ABC is the required triangle.

  4. Draw perpendicular bisector of BC which cuts BC at point O. With O as center and radius = OB, draw a circle.

  5. Draw angle bisector of ∠ABC which meets the circle at point P. Thus, point P is equidistant from AB and BC.

Measure ∠BCP.

Hence, ∠BCP = 30°.

Using a ruler and compasses only . (i) Construct a triangle ABC with the following data : AB = 3.5 cm, BC = 6 cm and ∠ABC = 120°. (ii) In same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC. (iii) Measure ∠BCP. Constructions, Concise Mathematics Solutions ICSE Class 10.

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