**Key Terms**

- Chord – Any line segment whose endpoints are on the circle.
- Diameter – A line segment that contains (passes through) the center of the circle and has endpoints on the circle.
- The diameter is a chord, as it has two endpoints ON the edge of the circle.
- This term also refers to the length of this line segment
- The diameter of a circle is twice the length of the radius.

**Review**

- Circumference – the distance around a circle
- To find the circumference, use or

- Perpendicular Bisector
- A line, ray, or segment
- Intersects a segment at its midpoint
- Forms right angles
- Divides a segment in half
- Is the shortest path between a line segment and a point not on that segment

**Notes**

- Chords
- Watch the video and draw an circle with chord .

- Congruence and Equidistance
- If two chords are the same distance from the center of a circle, then they must be congruent.
- If two chords of a given circle are congruent, then they must be equidistant from the center of the circle.

- Perpendicular Chords and Radii
- The shortest path between a line and any point (not on the line) is a path that is perpendicular to the line.
- If a radius of a circle bisects a chord, then it is perpendicular to that chord.
- If a radius of a circle is perpendicular to a chord, then it bisects that chord.

- Conditional Statement Proof
- Again, if a radius of a circle is perpendicular to a chord, then it bisects that chord.
- Prove that the Radius Bisects Chord

- Converse Statement Proof (true in this case)
- Again, if a radius of a circle bisects a chord, then it is perpendicular to that chord.
- Prove that the Radius is Perpendicular to Chord

- Template for Proofs

- Diameter
- Another name for a chord that passes through the center of a circle is the diameter.
- Changing the diameter of a circle changes the size of the circle because the diameter is two radii; and, the radius defines the size of the circle.

**Examples**

- Ex 1. In , radius intersects chord in point B so that AB = 8 units and BC = 8 units.
- This means that is perpendicular to .
- Try drawing this and marking congruency.

- Ex 2. Given below, you can conclude that is congruent to

- Ex 3. Given below, you can conclude that is congruent to

- Ex 4. If the blue radius below is perpendicular to the green chord and the segment is 9 units long, what is the length of the chord?
- Since has been bisected by the radius of the circle, is half of .
- and are congruent, so also equals 9.
- 9 + 9 = 18, so .

- Ex 5. The blue segment below is a radius of . What is the length of the diameter of the circle?
- Since the diameter is twice the length of the radius: 9.3(2) = 18.6 units is the length of the diameter.

- Ex 6. The blue segment below is a diameter of . What is the length of the radius of the circle?
- Since the diameter is twice the length of the radius: units is the length of the radius.