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