Mathematics 10 — Exercise 10.1 · Q3

Full question

Draw arc ABC and complete its circle by finding its centre.

Step-by-step solution

  1. Choose three distinct non-collinear points A,B,C on the given arc or circle. Join AB and BC.

  2. Open the compass to more than half AB. With A and B as centres and the SAME opening, draw intersecting arcs on both sides of AB.

  3. Join the two arc intersections. This is the perpendicular bisector of AB; every point on it is equally distant from A and B.

  4. Repeat the same compass construction for BC to obtain its perpendicular bisector.

  5. Name the intersection of the two bisectors O. Since OA=OB and OB=OC, OA=OB=OC. This identifies the unique centre.

  6. Set the compass opening to OA, keep its needle at O and draw the complete circle through A,B,C.

  7. Check that all three points lie on the completed circumference and that both bisectors pass through O.

Answer

The construction above gives the required circle or tangent.

OABCMNDiagram not to scale