QQuestionMathematics
QuestionMathematics
Which statement BEST defines a circle?
A) A circle is the set of all points in a plane equidistant from each other.
B) A circle is the set of all points in a plane equidistant from a given arc.
C) A circle is the set of all points in a plane equidistant from a given point.
D) A circle is the set of all points in a plane equidistant from a given segment.
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Understand the definition of a circle
A circle is a fundamental geometric shape defined by its unique property of point relationships in a plane.
Step 3:: Analyze the key components of a circle's definition
- The definition must involve: 1) Points in a plane 2) A consistent distance relationship 3) A reference point or element
Step 4:: Evaluate each option carefully
Option D: $$\text{Points equidistant from a given segment}
- This is incorrect because points equidistant from each other do not necessarily form a circle - Points could be scattered randomly in different arrangements - This is incorrect because an arc is a portion of a circle, not its defining characteristic - An arc cannot establish a consistent distance for all points - This is the CORRECT definition of a circle - The given point is called the "center" - All points on the circle are the same distance (radius) from this center point - This is incorrect because a line segment cannot establish a consistent distance for all points
Final Answer
C) A circle is the set of all points in a plane equidistant from a given point.
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