Question

Which of the following options are not steps involved in construction of circumcircle of the $△ABC$ with circumcentre $O$ ?

• A. Construction of the given triangle.
• B. Construction of perpendicular bisectors of the sides of the triangle.
• C. Construction of circle with radius OD (D is the midpoint of BC)
• D. Construction of circle with radius $2\times OA$

Answer 1

Answer: (C), (D)

The correct options are
C Construction of circle with radius OD (D is the midpoint of BC)
D Construction of circle with radius $2\times OA$

We first construct $△ABC.$
We then need to find the circumcentre of this triangle, i.e. the point of concurrence of the perpendicular bisectors of this triangle. Or in other words, we need to find the centre of the unique circle that passes through all 3 vertices of the triangle.
We next construct perpendicular bisectors of any two sides of the triangle, say AB and AC and name the point of concurrence as O.

Lastly, with the O as centre and OA (or OB or OC) as radius, construct the required circle.