The centre of circle passing through three non collinear points A,B,C is the concurrent point of

Options

A. Angle bisectors of `DeltaABC`
B. Perpendicular bisectors of the sides of `DeltaABC`
C. Altitudles of the `DeltaABC`
D. Medias of the `DeltaABC`

Answer

To find the center of the circle passing through three non-collinear points A, B, and C, we need to determine the point where the angle bisectors of the triangle formed by these points intersect. This point is known as the circumcenter of the triangle.

### Step-by-Step Solution:

1. **Identify the Points**: Let the three non-collinear points be A, B, and C. These points will form a triangle ABC.

2. **Construct the Triangle**: Draw triangle ABC using the points A, B, and C.

3. **Draw the Angle Bisectors**: For each angle of the triangle ABC (∠A, ∠B, and ∠C), draw the angle bisector. The angle bisector of an angle is a line that divides the angle into two equal parts.

4. **Find the Intersection of the Angle Bisectors**: The three angle bisectors will intersect at a single point. This point is known as the circumcenter of the triangle.

5. **Conclusion**: The circumcenter is the center of the circumcircle, which is the circle that passes through all three vertices of the triangle (points A, B, and C).

### Final Answer:
The center of the circle passing through the three non-collinear points A, B, and C is the concurrent point of all the angle bisectors of triangle ABC, which is called the circumcenter.

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