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That line is called diameter. It divides a circle into two semi circles.

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Q: What is the line through the center of a circle called?
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Does a secant line pass through the center of a 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.


What is the straight line through the center of a circle called?

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.


What is the name of a line drawn from one side of a circle to the other through the center?

This is called the diameter of the line that passes through the center of the circle. Half of that line is called the radius.


What is a line passing through the center of a circle with both end points on the circle called?

This is a line segment called a diameter of the circle.


What is a line through a circle that does not go through the center?

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.