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Mathematics

Using ruler and compasses only,

(i) Construct triangle ABC, having given BC = 7 cm, AB - AC = 1 cm and ∠ABC = 45°.

(ii) Inscribe a circle in the △ABC constructed in (i) above.

Constructions

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Answer

(i) Steps of construction :

  1. Draw a line segment BC = 7 cm.

  2. At B, draw a ray BX making an angle of 45° and cut off BE = AB - AC = 1 cm.

  3. Join EC and draw the perpendicular bisector of EC intersecting BX at A.

  4. Join AC.

Using ruler and compasses only, (i) Construct triangle ABC, having given BC = 7 cm, AB - AC = 1 cm and ∠ABC = 45°. (ii) Inscribe a circle in the △ABC constructed in (i) above. Constructions, Concise Mathematics Solutions ICSE Class 10.

Hence, ABC is the required triangle.

(ii) Steps of construction :

  1. Draw angle bisectors of ∠ABC and ∠ACB intersecting each other at O.

  2. From O, draw perpendicular OL to BC.

  3. With O as center and OL as radius draw a circle, touching sides of △ABC. Measure OL.

On measuring,

OL = 1.8 cm.

Hence, above is the required incircle of △ABC with radius = 1.8 cm.

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