Diameter
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A line through a circle that does not go through the center of the circle is a secant line. A line through a circle that does go through the center is still a secant line, by the way. Compare this to a line segment that has its two endpoints on the circumference of the circle. That line segment is a cord of the circle. If that cord of the circle passes through the center of the circle, then the cord is a diameter of that circle.
No, a secant line does not pass through the center of a circle. A secant line is a line that intersects a circle in two distinct points. Only a line passing through the center of a circle is called a diameter.
The line passing through the center of a circle with two endpoints on the circle is the circle's diameter.
The radius is the line from the center of a circle to its circumference.
A line that goes through a circle is a secant line. (Remember that a line is infinitely long.) Anyline that passes through a circle is a secant line, whether it passes through the center of the circle or not. Compare this to a line segment with endpoints on the circumference of a circle. That segment is called a cord of that circle. If the cord of a circle passes through the center of that circle, it is a diameter of that circle, which is the longest cord of the circle.