G.C.A.2 STUDENT NOTES & PRACTICE WS #4 – geometrycommoncore.com 1
Advanced Tangent Problems
Theorem – If a line is tangent to a given circle, then the tangent line
is perpendicular to the radius at the point of tangency.
Most of these advanced problems use the Pythagorean Theorem because it can be applied to
the right triangle formed by a tangent line and the radius.
EXAMPLE #1 – Given that
BC
is tangent to the circle A, find x.
2 2 2
22
15 ( 9)
225 18 81
225 18 81
8
xx
x x x
x
x
EXAMPLE #2 – Given that
AB
is tangent to circle D, find x.
Create a parallel line to
AB
.
62 + x2 = 82 x =
28 2 7 5.29
NYTS (Now You Try Some)
1. Given that
CD
is tangent to circle A & circle B, find x.
m
A
B
x
9 cm
15 cm
x
A
B
C
8 cm
x
2 cm
8 cm
B
D
A
2 cm
8 cm
x
2 cm
6 cm
B
A
10 cm
x
6 cm
4 cm
A
C
D
B
Answers: 1. Similar triangles are formed by AA….. thus x = 5.
