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Question

# How many circles can be drawn passing through 3 non-collinear points ?

A

Infinite

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B

1

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C

0

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D

4

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Solution

## The correct option is B 1 Through a single point P, infinite number of circles passing through it can be drawn. Let us now consider 2 points. Again, we see that infinite number of circles passing through points P and Q can be drawn. Let us now take 3 points. If the points are collinear, then there is no circle that passes through all of them. In this case, one of the 3 points would lie inside or outside the circle drawn passing through the other two points. Let us consider the case where the points are non-collinear. It can be shown that there is one and only circle passing through all 3 points.

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