Question

Assertion: Through 3 non collinear points A, B, C many circles can be drawn.

Reason: The 2 perpendicular bisectors of AB and BC meet at one point which is the centre of the circle.

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

The assertion is false because through 3 non-collinear points, only one circle can be drawn, not many circles. The reason is true because the two perpendicular bisectors of sides AB and BC intersect at a single point, which is the center of the circle passing through these three points. This single intersection point is equidistant from A, B, and C, so only one unique circle can be drawn. Thus, the correct reasoning is that exactly one circle passes through three non-collinear points because the two perpendicular bisectors intersect at a unique point, the center of the circle.