A line is perpendicular to a chord of a circle

In the applet below, drag the line to either bisect the chord or to make it pass through the centre of the circle.

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If any two of the statements are true, the remaining statement is true.

If a line is perpendicular to a chord of the circle and passes through the centre of a circle, then the line bisects that chord of a circle.

If a line is perpendicular to a chord of a circle and bisects that chord of that circle, then the line passes through the centre of the circle.


If a line is perpendicular to a chord of the circle and does NOT pass through the centre of a circle, then the line does NOT bisect that chord of a circle.

If a line is perpendicular to a chord of a circle and does NOT bisect that chord of that circle, then the line does NOT pass through the centre of the circle.