Download Notes 11.4 - Warren County Schools

Geometry Bell ringer
March 20, 2012
Find the indicated angle measures.
63
x
230
y
Homework Answers
1)87
2)35
3)45
4)120
5)72
6)186
7)80
8)30; 30; 120
Vocabulary
• Secant – a line that intersects a circle at
two points. (could be a secant line,
secants ray, or secant segment)
A
Does a secant always contain
a chord of the circle?
Yes, the segment between the
two points that intersect with
the circle is a chord
B
Theorem
x°
Are there any other
intercepted arcs?
1
y°
Theorem
• The measure of an angle formed by two
secants, tangents, or a secant and a tangent
drawn from a point outside the circle is half the
difference of the measures of the intercepted
arcs.
1
yº
xº
yº
xº
1
yº
xº
1
Theorems
• If two chords intersect inside a
circle, then the product of the
lengths of the segments of one
chord equals the product of the
lengths of the segments of the
other chord.
c
a
a(b) = c(d)
b
d
Theorem
If two secant segments are
drawn from a point outside
a circle, the product of the
lengths of one secant
segment and its external
segment equal the product
of the lengths of the other
secant segment and its
external segment.
x
w
y
(w + x)w = (y + z)y
z
Theorem
If a tangent and a secant are drawn from a point
outside a circle, then the product of the lengths
of the secant segment and its external segment
equals the square of the length of the tangent
segment.
t
(y + z)y = t2
y
z