Show that the line passing through the center of a circle and the mid point of a chord is perpendicular to that chord, provided the chord is not a diameter.

I would appreciate any help on this proof...

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- Feb 7th 2010, 03:35 PMmdkChord and Circle
Show that the line passing through the center of a circle and the mid point of a chord is perpendicular to that chord, provided the chord is not a diameter.

I would appreciate any help on this proof... - Feb 7th 2010, 07:26 PMNRS
I haven't done proofs in a long time, but first I would say that you have to define all of your points, such as AB is one segment in the chord, CD is another segment in the chord, and XY crosses the chord at the points L and M.

Gather any and all theorems that you would need. You know that logicaly the line has to be perpendicular to the chord, because passing through the midpoint of the chord, means that you are making a diameter of the circle.

Maybe you could try proving that the length of AL is the same length as BL, and that CM and DL are equal, meaning that you are going to have right angles wherever XY intersects the chord..... - Feb 7th 2010, 08:22 PMpragraphic
think about creating 2 trangles

and show proof of this 2 trangles are SSS

then the adj angles of on chord are equal

so they are 90 degree

and thus two lines are perpendicular