Integrated Math 2 / Unit 8: Circles
8.2 Chords and Arcs
Notes
A chord is a segment joining two points on a circle.
- Congruent chords have congruent arcs, and the reverse is true.
- A radius or diameter perpendicular to a chord bisects the chord.
- Example: radius 10, a chord 6 units from the center: half the chord is $\displaystyle \sqrt{10^2 - 6^2} = 8$, so the chord is 16.
- Chords crossing inside a circle: the products of the segments are equal. If segments are $a, b$ and $c, d$, then $ab = cd$.
Practice
A circle has radius 10. A chord is 6 units from the center. How long is the chord?
Half the chord is $\displaystyle \sqrt{10^2 - 6^2} = 8$, so the chord is 16.
Two chords cross inside a circle. One is split into segments 4 and 6. The other is split into 3 and $x$. Find $x$.
$4 \cdot 6 = 3 \cdot x$, so $x = 8$.
Two chords in the same circle are congruent. Which must be true?
In one circle, congruent chords cut off congruent arcs.
Ready for more? Take the Unit 8 test.