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# Chords and a Circle's Center - Concept

###### Brian McCall

###### Brian McCall

**Univ. of Wisconsin**

J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

A chord is a line segment whose endpoints are on a circle. If a chord passes through the center of the circle, it is called a diameter. Two important facts about a **circle chord** are that (1) the perpendicular bisector of any chord passes through the center of a circle and (2) congruent chords are the same distance (equidistant) from the center of the circle.

Chords in the center of a circle have a special relationship but back up what's a chord? Let's refresh our memory. Well a chord is a line segment whose endpoints are on the circle. 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.

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 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. So using these two keys about chords and the relationship with the center will help us solve a lot of problems.

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###### Brian McCall

B.S. in Chemical Engineering, University of Wisconsin

J.D. University of Wisconsin Law School (magna cum laude)

He doesn't beat around the bush. His straightforward teaching style is effective and his subtle midwestern accent is engaging. There's never a dull moment with him.

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