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Easy
Normal
Intercept Theorem - Problems with Solutions
Problem 1
The line
CD
is parallel to
AB
and crosses the angle
BOA
so that
O,B,D
lie on the same line and so do
O,A,C
. If
AB=5
,
OB=3
and
OD=12
, determine the length of
CD
.
Solution:
The lines
AB
and
CD
are parallel, so by the intersect theorem, we have [tex]\frac{OD}{OB}=\frac{CD}{AB}[/tex], or [tex]CD=\frac{OD}{OB}.AB=\frac{12}{3}.5=20[/tex].
Problem 2
The line
CD
is parallel to
AB
and crosses the angle
BOA
so that
O,B,D
lie on the same line and so do
O,A,C
. If
AB=5
,
OA=5
and
OC=8
, determine the length of
CD
.
Solution:
The lines
AB
and
CD
are parallel, so by the intersect theorem, we have [tex]\frac{OC}{OA}=\frac{CD}{AB}[/tex], or [tex]CD=\frac{OC}{OA}.AB=\frac{8}{5}.5=8[/tex].
Problem 3
The line
CD
is parallel to
AB
and crosses the angle
BOA
so that
O,B,D
lie on the same line and so do
O,A,C
. If
OA=2
,
OB=5
and
OD=15
, determine the length of
OC
.
Solution:
The lines
AB
and
CD
are parallel, so by the intersect theorem, we have [tex]\frac{OA}{OB}=\frac{OC}{OD}[/tex], or [tex]OC=\frac{OA}{OB}.OD=\frac{2}{5}.15=6[/tex].
Problem 4
The line
CD
is parallel to
AB
and crosses the angle
BOA
so that
O,B,D
lie on the same line and so do
O,A,C
. If
OA=5
,
AC=3
and
BD=6
, determine the length of
OB
.
Solution:
The lines
AB
and
CD
are parallel, so by the intersect theorem, we have [tex]\frac{OB}{BD}=\frac{OA}{AC}[/tex], or [tex]OB=\frac{OA}{AC}.BD=\frac{5}{3}.6=10[/tex].
Problem 5
The line
CD
is parallel to
AB
and crosses the angle
BOA
so that
O,B,D
lie on the same line and so do
O,A,C
. If
OA=2
,
AC=4
and
BD=6
, determine the length of
OB
.
Solution:
The lines
AB
and
CD
are parallel, so by the intersect theorem, we have [tex]\frac{OB}{BD}=\frac{OA}{AC}[/tex], or [tex]OB=\frac{OA}{AC}.BD=\frac{2}{4}.6=3[/tex].
Easy
Normal
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