Question

draw or lose Trilliceture de​

Answer 1

Answer:

To draw a straight line the minimum number of points required is two. Given any two points, a straight line can be drawn. How many minimum points are sufficient to draw a unique circle? Well, let’s try to find out.

Circle Passing Through a Point

Let us consider a point and try to draw circle passing through that point.

Circle - Circle passing

It can be seen that through a single point P infinite circles passing through it can be drawn.

Circle Passing Through Two Points

Now, let us take two points P and Q and see what happens?

Circle passing through PQ

Again we see that an infinite number of circles passing through points P and Q can be drawn.

Circle Passing Through Three Points (Collinear or Non-Collinear)

Let us now take 3 points. For a circle passing through 3 points, two cases can arise.

Three points can be collinear

Three points can be non-collinear

Let us study both cases individually

Answer 2

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Let D, E, F be the collinear points. The perpendicular bisector of DE and EF drawn (i.e., line l and line m) do not intersect at a common point. ∴ There is no single common point (centre of circle) from which a circle can be drawn passing through points D, E and F. Hence, we cannot draw a circle passing through points D, E