Part A: A circle is the set of all points that are the same distance from one given point. Find an example that contradicts this definition. How would you change the definition to make it more accurate? (5
points)
Part B: Give an example of an undefined term and how it relates to a circle. (5 points)



Answer :

Final answer:

An ellipse contradicts the definition of a circle, and an improved definition clarifies equidistance from a fixed center. The undefined term 'tangent' is related to a circle by intersecting it at precisely one point.


Explanation:

Circle Contradiction Example: An example that contradicts the definition of a circle is an ellipse. An ellipse is defined as the set of points where the sum of the distances from two fixed points is constant, not necessarily the same distance from one given point.

Improved Circle Definition: A circle can be accurately defined as the set of all points that are equidistant from a single fixed point, known as the center. This definition clarifies that every point on the circle is at the same distance from the center.

Undefined Term Related to Circle: An undefined term related to a circle is a tangent. A tangent is a line that intersects a circle at exactly one point. In geometry, a circle and a tangent have a unique relationship where the tangent line is perpendicular to the radius at the point of tangency.


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