Graphics Reference
In-Depth Information
Figure 6.21.
Circles of fixed radius tangent to two lines.
Figure 6.22.
Lines through a point tangent to a circle.
6.8.3 Formula.
Let
A
be a point and
C
a circle with center
B
and radius r. Assume
that |
AB
|>r. There are two lines through
A
that are tangent to
C
and they intersect
C
in the points
D
±
defined by
2
2
DA
AB
AB
-
r
r
2
2
±
=+
u
±
AB
-
r,
v
AB
where
u
and
v
are the orthonormal vectors
AB
AB
u
=
=
(
u
,
u
)
and
v
=
(
u
,
u
)
.
12
21
Proof.
Figure 6.22(a) shows the two lines
L
and
L
¢ that pass through
A
and are
tangent to
C
. By switching to the coordinate system defined by the frame (
A
,
u
,
v
) we
may assume that
A
= (0,0) and
B
= (b,0). Let
D
= (d
1
,d
2
). See Figure 6.22(b). The fol-
lowing equations are satisfied by
D
:
