Civil Engineering Reference
In-Depth Information
In Figure 5-41, draw diameters
MS
and
LF
at right angles to each
other. At points
M
,
L
,
S
, and
F
, where these diameters intersect the
circle, draw tangents (that is, lines perpendicular to the diameters),
obtaining the sides of the circumscribed square
ABCD
.
L
A
B
M
S
D
C
F
Figure 5-41
To circumscribe a square about a circle.
Problem 22
To inscribe a circle in a triangle.
In Figure 5-42, bisect two angles
A
and
C
of the triangle with
lines that intersect at
D
. From
D
, draw a perpendicular
DE
to any
side. With
DE
as the radius, describe a circle.
Problem 23
To inscribe a pentagon in a circle.
In Figure 5-43, draw two diameters
AC
and
BD
at right angles
intersecting at
O
. Bisect
AO
at
E
, and from
E
, with radius
EB
,
AC
at
F
; from
B
, with radius
BF
. Intersect the circumference at
G
and
H
, and with the same radius, step round the circle to
I
and
K
; join
the points thus found to form the pentagon
BGIKH
.
Problem 24
To inscribe a five-pointed star in a circle.
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