So using these two keys about chords and the relationship with the center will help us solve a lot of problems. If I found the perpendicular bisector of these chords so if I measured the perpendicular distance from the chord to the center, so I'm going to draw a solid line here so this is the perpendicular distance because we said the shortest distance between two points is a line to perpendicular, if these chords are congruent, they will be the same distance away from the center of the circle so if I were to join two other chords and if I told you that these chords are congruent then their distance from the center of that circle measured along a perpendicular will be congruent. ![]() Let's talk about 2 congruent chords, so this is kind of a converse of what we just talked about. If I found the perpendicular bisector of this chord so if I took my compass and I swung arcs from both ends of that and I found the line that bisected this chord into two congruent pieces at a 90 degree angle, so let's say I do that in so this dotted line is my perpendicular bisector of that chord and no matter where I draw a chord on this circle if I find it's perpendicular bisector it will always pass through the center of the circle so that's the first key thing about a chord as relationship with the center of circle. Chord Theorem 2: The perpendicular bisector of a chord is also a diameter. In both of these pictures, B E C D and B E C D. Well a chord is a line segment whose endpoints are on the circle. Chord Theorem 1: In the same circle or congruent circles, minor arcs are congruent if and only if their corresponding chords are congruent. Chords in the center of a circle have a special relationship but back up what's a chord? Let's refresh our memory.
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