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Using ruler and compasses only, construct a triangle ABC in which BC = 4 cm, ∠ACB = 45° and the perpendicular from A on BC is 2.5 cm. Draw the circumcircle of triangle ABC and measure its radius.

Constructions

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Answer

Steps of construction :

  1. Draw a line segment BC = 4 cm.

  2. At B, draw a perpendicular and cut off BE = 2.5 cm.

  3. From E, draw a line EF parallel to BC.

  4. From C, draw a ray making an angle of 45° which intersects EF at A.

  5. Join AB.

  6. Draw a line AD parallel to BE. This AD is the perpendicular bisector of BC.

  7. Draw the perpendicular bisectors of sides BC and AC intersecting at O.

  8. With centre O and radius OB or OC or OA draw a circle which will pass through A, B and C. This is the circumcircle of △ABC.

Using ruler and compasses only, construct a triangle ABC in which BC = 4 cm, ∠ACB = 45° and the perpendicular from A on BC is 2.5 cm. Draw the circumcircle of triangle ABC and measure its radius. Constructions, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

On measuring OB we get the radius of the circumcircle.

Hence, the radius of circumcircle = 2 cm.

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