Answer
376.2k+ views
Hint: To solve this question are should have knowledge of collinear points always lie in the same line while non-collinear never occurs all in the same line. Try drawing a circle or more using the given points and then check how many are possible.
We will first of all define certain terms to solve this question.
Collinear points – Three or more points are said to be collinear if they lie in the same straight line.
For example: In the figure below the points A, B and C are collinear.
Non – collinear point – Three or more points are called non – collinear points if they do not lie in the same straight line.
Example: In the figure below P, Q and R are non-collinear.
Here in this question, we are given three non-collinear points; let it be P, Q, and R. We will follow certain steps of construction to draw a circle using these points,
Step 1: Join PQ and QR.
Step 2: Using a compass draw perpendicular bisectors of line PQ and line QR. Name them as MN & ST respectively.
Le the point where they meet name as O.
Step 3: Taking O as the point on the compass and radius as OP draws a circle.
We have obtained only one circle using these three non-collinear points P, Q, and R.
Therefore only one circle can be obtained using three non-collinear points, which is an option (a).
Note: If the student has any possibility of confusion in the number of possible circles, then they can go for drawing more different perpendicular bisection the center O would anyway be the same. Hence the circle would also be the same. Therefore only one circle is possible.
We will first of all define certain terms to solve this question.
Collinear points – Three or more points are said to be collinear if they lie in the same straight line.
For example: In the figure below the points A, B and C are collinear.
![seo images](https://www.vedantu.com/question-sets/bb22867b-b75d-4687-a6aa-520f30f6c0645480254961271535671.png)
Non – collinear point – Three or more points are called non – collinear points if they do not lie in the same straight line.
Example: In the figure below P, Q and R are non-collinear.
![seo images](https://www.vedantu.com/question-sets/a514c4f5-29a4-475c-8adc-31f20d5731c83905569485679806138.png)
Here in this question, we are given three non-collinear points; let it be P, Q, and R. We will follow certain steps of construction to draw a circle using these points,
![seo images](https://www.vedantu.com/question-sets/652edac8-0ecd-4b41-860f-0595ad23297a2008042068301718362.png)
Step 1: Join PQ and QR.
![seo images](https://www.vedantu.com/question-sets/529d5a58-c721-4259-a5da-c8d08c407daa754797279548603786.png)
Step 2: Using a compass draw perpendicular bisectors of line PQ and line QR. Name them as MN & ST respectively.
![seo images](https://www.vedantu.com/question-sets/e7faec7c-f9ba-46d2-9bf8-caa700e92a0d6911051111130951267.png)
Le the point where they meet name as O.
Step 3: Taking O as the point on the compass and radius as OP draws a circle.
![seo images](https://www.vedantu.com/question-sets/d2a340c8-1632-4f5e-99f9-f1596aa981016866866032800387104.png)
We have obtained only one circle using these three non-collinear points P, Q, and R.
Therefore only one circle can be obtained using three non-collinear points, which is an option (a).
Note: If the student has any possibility of confusion in the number of possible circles, then they can go for drawing more different perpendicular bisection the center O would anyway be the same. Hence the circle would also be the same. Therefore only one circle is possible.
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