Question

The number of circles that can pass through 3 non collinear points is :
A. One
B. Two
C. Many
D. None .

Answer 1

Hint: Try to think of what figure you can form with three non collinear points and how many circles are associated with that figure

Complete step-by-step answer:
The circumcircle is a circle that passes through all 3 vertices of a triangle and contains the triangle inside it . This circle is special because every triangle can have only ONE circumcircle.
Now , according to the above question , 3 non collinear points is another way of mentioning a triangle . Since the only circle that passes through all 3 points (vertices ) is a circumcircle , the correct option is A .
It is important to note the use of the word non collinear , no circle could have passed through all three points .

Note: Knowledge and memory of circumcircle of a triangle is required. Also, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle, it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle's incenter.