Acircle is the collection of points in a plane that are the same distance from a given point in the plane. true or false

true

any given point in a circle is equal distance from the center

TRUE.

Step-by-step explanation:

It knows that the distance "d" between any two points is equal to .

In a circle the distance between a point that belongs to the circumference and the center () is always the same. Then:

is always equal to a constant called "r".

This is:

Square both sides of the equality:

Note that we obtain the General equation of a circle.

This prove that if the distance between a given point in the plane and a collection of points is equal, then the equation of a circle is obtained.

Therefore, the statement "A circle is the collection of points in a plane that are the same distance from a given point in the plane." is true.

step-by-step explanation: