Math  /  Geometry

QuestionThree non-collinear points (x1,y1),(x2,y2)\left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right), and (x3,y3)\left(x_{3}, y_{3}\right) determine a circle because: - A. They are equidistant from the circle's center. - B. They form the radius of a circle. - C. They lie on the perpendicular bisectors of the triangle formed. - D. They define a parabola.

Studdy Solution
Conclude with the correct option: - The correct explanation for why three non-collinear points determine a circle is **Option C**. They lie on the perpendicular bisectors of the triangle formed, which intersect at the circumcenter of the circle.
The correct answer is:
C \boxed{\text{C}}

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