Question

ABC is a triangle. Number of circles that can be drawn circumscribing this triangle is/are ?

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is B

1

For the triangle ABC, draw perpendicular bisectors for AB and AC. Let the point of intersection of these two lines be O.

Since we know that any point on the perpendicular bisector of a line segment is equidistant from the endpoints of the line segment, OA=OB and OB=OC. Thus OA=OB=OC. Now if we draw a circle with O as center and OA as radius it will pass through points B and C.

Since two lines can intersect at only one point only one circle can be drawn circumscribing the triangle.