10A.notebook
March 13, 2013
more walk arounds #1
Circles A, B, and C are tangent. Find each radius if
AB = 8
BC = 13
AC = 11
8
Circles A, B, and C are tangent. Find each radius if
AB = 15
BC = 17
AC = 12
B
B
A
A
13
11
C
C
walk around radii
walk around radii
Example:
Find the common external tangent of two circles with
radii 3m and 10m if the centers are 25m apart.
Tips for common tangents.
.
1)
Draw 2 circles and the common tangent
.
2)
Draw radii perpendicular to the tangents
.
3)
Connect the centers (if you haven't already)
.
4)
Create a rectangle and right triangle
.
T
QUAD is tangent to OO.
QU = 18
UA = 14
QD = 17.
Q
2) Draw radii to the tangents
1) Draw 2 circles and the common tangent
U
x
x
10
3
Find AD.
O
3) Create a rectangle and right triangle
.
4) Connect the centers (if you haven't already)
A
x
D
3 10
7
x
3
25
To tangent segments drawn from the same point are congruent.
5) Solve
x
3
x
3 10
7
x
7
25
25
x = 24
walk around tangents
Common Tangents
10A.notebook
March 13, 2013
.
Common external tangent ‐ Overlapping OO's.
Ex: The centers of 2 circles of radii 10 and 4 are 12 units apart. Find the length of the common external tangent.
Mar 12­10:57 AM
.
Common external tangent ‐ Tangent OO's.
Ex: The two circles are externally tangent, Circle O has radius 9, circle P has radius 4.
Find the length of the common external tangent.
comm ext tan
Common INTERNAL Tangent
Find the length of the common internal tangent of 2 circles with radii 5 cm and 1 cm if the centers are 10cm apart.
A radius drawn to a tangent is perpendicular at the point of tangency
.
.
comm ext tan
Mar 13­1:22 PM