QuestionThree non-collinear points , and 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
STEP 1
1. We have three non-collinear points: .
2. We need to determine which statement correctly explains why these points determine a circle.
STEP 2
1. Understand the geometric property of a circle related to points.
2. Analyze each option to determine which one correctly explains the property.
3. Conclude with the correct option.
STEP 3
Understand the geometric property of a circle related to points: - A circle is defined as the set of all points that are equidistant from a given point, called the center.
STEP 4
Analyze each option:
- **Option A**: They are equidistant from the circle's center.
- This is a correct statement about points on a circle. All points on a circle are equidistant from the center.
- **Option B**: They form the radius of a circle.
- This statement is incorrect. The radius is a line segment from the center to any point on the circle, not formed by three points.
- **Option C**: They lie on the perpendicular bisectors of the triangle formed.
- This statement is related to the circumcircle of a triangle. The perpendicular bisectors of the sides of a triangle intersect at the circumcenter, which is equidistant from the vertices.
- **Option D**: They define a parabola.
- This statement is incorrect. Three points do not define a parabola unless they are collinear and one is the vertex.
STEP 5
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:
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