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Mathematics

(i) Using ruler and compasses only, construct a triangle ABC in which AB = 8 cm, BC = 6 cm and CA = 5 cm.

(ii) Find its incenter and mark it I.

(iii) With I as centre, draw a circle which will cut off 2 cm chords from each side of the triangle.

Constructions

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Answer

Steps of construction :

  1. Draw a line segment BC = 6 cm.

  2. With B as center and radius 8 cm draw an arc.

  3. With C as center and radius 5 cm draw another arc which intersects first arc at A.

  4. Join AB and AC. ABC is the required triangle.

  5. Draw angle bisectors of B and A intersecting each other at I. I is the incenter.

  6. Through I, draw ID ⊥ AB.

  7. From D as center cut off DP = DQ = 22\dfrac{2}{2} = 1 cm.

  8. With I as center and radius IP or IQ, draw a circle cutting off 2 cm chords from each side of triangle.

(i) Using ruler and compasses only, construct a triangle ABC in which AB = 8 cm, BC = 6 cm and CA = 5 cm. (ii) Find its incenter and mark it I. (iii) With I as centre, draw a circle which will cut off 2 cm chords from each side of the triangle. Constructions, Concise Mathematics Solutions ICSE Class 10.

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