The document outlines rules for determining the size of angles formed by intersecting lines in circles. It provides formulas to calculate angles formed by two secants intersecting inside or outside a circle, a secant and tangent, and two tangents. It also describes relationships for products of chord segments, secant segments, and secant and tangent segments.

1. 13.notebook September 26, 2012
Rules to determine the size of an angle formed by:
2 secants intersecting inside a circle HALF THE
SUM OF
40 + 80 = 60o
40 o x 80 o x = 2
THE ARCS
2 secants intersecting outside a circle
x 80 o x = 80 ­ 40 = 20o
40o 2
a secant and a tangent HALF THE
DIFFERENCE
x o
x = 120 ­ 60 = 30o OF
60 120 o
2
THE ARCS
two tangents
260o
x = 260 ­ 100 = 80
o
100o
2
x
1

2. 13.notebook September 26, 2012
Products of chord segments
3 6
3 8 = 4 6
4
8
Product of secant segments
(secants length external length)
3 5
8(3) = 12(2) =
(secants length external length)
2 10
Product of secant and tangent segments
12
(secants length external length)
4 16(4) = 8(8) =
(tangent length squared)
8
2

3. 13.notebook September 26, 2012
1. Find x.
x
3
x 3
3

4. 13.notebook September 26, 2012
2. Find x.
12
x
8
4