2. 10.6 Find Segment Lengths in Circles
discovery time!
complete the 10.6 Clock activity sheet

3. Theorem:
If two ________ intersect in a circle, then the _________ of the measures of the ___________ of the chords are ___________.
Therefore, ______________
chords
products
equal
segments
ad = bc

4. More Theorems: Terms for next two theorems: secant segments:
external secant segments:
A segment from a point exterior to a circle to a point on the circle and containing a chord of the circle (AC or AD).
Part of a secant segment that is exterior to the circle (AB or AE).
If two ______ segments are drawn to a circle from an ________ point, then the ___________of the measures of one secant segment and its __________ secant segment is _________ to the product of the measures of the other secant segment and its external secant segment.
External Secant Segments: ________ and _______
so that basically… __________ = _____________
secant
exterior
product
equal
external AE AB
AC*AB
AD*AE
(CB + BA) BA = (DE + EA) EA

5. More Theorems:
If a ________ segment and a _______ segment are drawn to a circle from an ________ point, then the _______ of the measure of the _______ segment is ______ to the _______ of the measures of the secant segment and its external secant segment.
Basically… ________ = ___________
tangent
secant
square
external
tangent
equal
product
XZ*XY XW 2
(ZY + YX)YX

6. Examples (x+3)3 = (7+4)4 9x = 18 3x + 9 = 44 x = 2 x = 11.7
Find the value of x to the nearest tenth. Assume that the segments that
appear to be tangent are tangent:
(x+3)3 = (7+4)4
9x = 18
3x + 9 = 44
x = 2
x = 11.7

7. Examples (9+4)4 = x² (6+x+3)6 = 12² X = 7.2 54+6x = 144 X = 15
Find the value of x to the nearest tenth. Assume that the segments that
appear to be tangent are tangent:
(9+4)4 = x²
(6+x+3)6 = 12²
X = 7.2
(9+x)6 = 144
54+6x = 144
X = 15
2y = 15*3
y = 22.5

8. Homework ws

9. THAT'S ALL FOR TODAY!