1. 8.1 Circle Terminology and Chord Properties
This section will introduce you to some of the most important aspects of circle geometry
Chord
Tangent
Diameter
Radius

2. Circle Terminology Circumference – The perimeter of a circle
Radius – A segment connecting the center of a circle with a point on the circle
Diameter – A segment that goes through the center of the circle and connects to two points on the outside of the circle
Chord – A segment whose end points are on the circle
Tangent – A line that intersects the circle on exactly one point

3. Important Formulas
The sum of the interior angles of a triangle is 180°
The number of degrees in a circle is 360°
Circumference = πd = 2πr
Area of a circle = πr2
Pythagorean Theorem states that the sum of the squares of the legs of a right triangle is equal to the square of its hypotenuse a2 + b2 = c2
180°
360° c a b

4. Formulas in Action Example 1: Find angle B Solution 1:
ΔABC is isoceles, so ∟B = ∟C
∟A + ∟B + ∟C = 180°
50° + ∟B + ∟B = 180°
2(∟B) = 130°
∟B = 65°
Example 2: Find BC
Solution 2:
Use the Pythagorean Theorem
Let BC be x
x2 =
x2 = = 169
x = = 13
Therefore BC = 13 B A 5
50° A C 12 B C

5. Some Important Chord Properties
The Diameter perpendicular to a chord bisects the chord and its arc
If AB CD, then CE = ED
The perpendicular bisector of a chord passes through the center of the circle
If AB CD and AE = EB, then CD passes through the center of the circle A C D E B C A B E D