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ICSE Question Bank
2016Q8(b)(i)Constructions (Circles)
ConstructionModerate2 marks
8(b)

Draw a line AB = 5 cm. Mark a point C on AB such that AC = 3 cm. Using a ruler and a compass only, construct :

A circle of radius 2.5 cm, passing through A and C.

Topic: Geometrical construction

Previous-year question practice database

Answer

Solution diagram
Solution diagram
Exam answer

Construction:

  1. Draw AB = 5 cm.
  2. Mark C on AB such that AC = 3 cm.
  3. Construct the perpendicular bisector of AC.
  4. Since the required radius is 2.5 cm, take A as centre and radius 2.5 cm and draw an arc cutting the perpendicular bisector of AC at O.
  5. With O as centre and radius 2.5 cm, draw the circle through A and C.

Answer:

Required circle constructed.

Explanation

The centre of a circle passing through A and C must be equidistant from A and C, so it lies on the perpendicular bisector of AC. Its distance from A and C must also equal the given radius 2.5 cm.

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