This preview shows page 1. Sign up to view the full content.
64
Chapter 2
•
General Triangles
§2.5
Example 2.19
Find the radius
r
of the inscribed circle for the triangle
△
ABC
from Example 2.6 in Section 2.2:
a
=
2,
b
=
3, and
c
=
4. Draw the circle.
O
A
B
C
Figure 2.5.8
Solution:
Using Theorem 2.11 with
s
=
1
2
(
a
+
b
+
c
)
=
1
2
(2
+
3
+
4)
=
9
2
, we have
r
=
r
(
s
−
a
)(
s
−
b
)(
s
−
c
)
s
=
R
±
±
²
(
9
2
−
2
) (
9
2
−
3
) (
9
2
−
4
)
9
2
=
³
5
12
.
Figure 2.5.8 shows how to draw the inscribed circle: draw the
bisectors of
A
and
B
, then at their intersection use a compass
to draw a circle of radius
r
=
r
5/12
≈
0.645.
Exercises
For Exercises 16, ±nd the radii
R
and
r
of the circumscribed and inscribed circles, respectively, of
the triangle
△
ABC
.
1.
a
=
2,
b
=
4,
c
=
5
2.
a
=
6,
b
=
8,
c
=
8
3.
a
=
5,
b
=
7,
C
=
40
◦
4.
A
=
170
◦
,
b
=
100,
c
=
300
5.
a
=
10,
b
=
11,
c
=
20.5
6.
a
=
5,
b
=
12,
c
=
13
For Exercises 7 and 8, draw the triangle
△
ABC
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.
 Fall '11
 Dr.Cheun
 Calculus, Angles

Click to edit the document details