1. Lesson 10-R
Chapter 10 Review

2. Objectives
Review Chapter 10 material

3. Parts of Circles Circumference (Perimeter) Chord Radius Diameter
once around the outside of the circle; Formulas: C = 2πr = dπ
Chord
segment with endpoints of the edge of the circle
Radius
segment with one endpoint at the center and one at the edge
Diameter
segment with endpoints on the edge and passes thru the center
longest chord in a circle
is twice the length of a radius
Other parts
Center: is also the name of the circle
Secant: chord that extends beyond the edges of the circle
Tangent: a line (segment) that touches the circle at only one point

4. Arcs in Circles Arc is the edge of the circle between two points
An arc’s measure = measure of its central angle
All arcs (and central angles) have to sum to 360°
If two arcs have the same measure then the chords that form those arcs have the same measure
If a radius is perpendicular to a chord then it bisects the chord and the arc formed by the chord (example arc AED below)
Major Arc (example: arc DAB)
measures more than 180°
more than ½ way around the circle
Minor Arc (example: arc AED)
measures less than 180°
less than ½ way around the circle
Semi-circle (example: arc EAB)
measures 180°
defined by a diameter
BE is a diameter
and AB = AD
120° B A C
120°
60° E D
60°

5. Angles Associated with Circles
Name
Vertex Location
Sides
Formula
Example
Central
Center
radii
= measure of the arc
BCD = 110°
Inscribed
Edge
chords
= ½ measure of the arc
BAD = 55°
Interior
Inside
= average of the vertical arcs
EVH = 73°
Exterior
Outside
Secants / Tangents
= ½ (Big Arc – Little Arc)
= ½ (Far Arc – Near Arc)
NVM = 30°
minor arc LK = 10°
minor arc NM = 70° E G F C
110° H
36° V
minor arc FG = 110°
minor arc EH = 36° V K L M N A D B C
110°
minor arc BD = 110°
10° C
70°

6. Segments Inside/Outside of Circles
Segments that intersect inside or outside the circle have the length of their parts defined by:
Two Chords Inside a Circle
Two Secants From Outside Point
Secant & Tangent From Outside Point J J K 4 5 3 6 L K K 3 L 4 J T 8 9 7 6 11 N N M M M
LJ · JM = NJ · JK
3  8 = 6  4
JL · JN = JK · JM
5  12 = 4  15
JT · JT = JK · JM
6  6 = 3  12
Inside the circle, it’s the parts of the chords multiplied together
Outside the circle, it’s the outside part multiplied by the whole length
OW = OW

7. Tangents and Circles Tangents and radii always form a right angle
We can use the converse of the Pythagorean theorem to check if a segment is tangent
The distance from a point outside the circle along its two tangents to the circle is always the same distance S T J C
Example 1
Given:
JT is tangent to circle C
JC = 25 and JT = 20
Find the radius
Example 2
Given:
same radius as example 1
JC = 25 and JS = 16
Is JS tangent to circle C?
JC² = JT² + TC²
25² = 20² + r²
625 = r²
225 = r²
15 = r
JC² = JS² + SC²
25² = 16² + 15²
625 =
625 ≠ 481
JS is not tangent

8. Equation of Circles
A circle’s algebraic equation is defined by: (x – h)² + (y – k)² = r² where the point (h, k) is the location of the center of the circle and r is the radius of the circle
Circles are all points that are equidistant (that is the distance of the radius) from a central point (the center)
Midpoint of the endpoints of diameter is the center
Distance formula between the center and a point on the circle can find the radius

9. Summary & Homework Summary: Homework:
All my life’s a circle -- Harry Chapin
Homework:
study for the test