MENU
❌
Home
Math Forum/Help
Problem Solver
Practice
Algebra
Geometry
Tests
College Math
History
Games
MAIN MENU
1 Grade
Adding and subtracting up to 10
Comparing numbers up to 10
Adding and subtracting up to 20
2 Grade
Adding and Subtracting up to 100
3 Grade
Addition and Subtraction up to 1000
Multiplication up to 5
Multiplication Table
Rounding
Dividing
Perimeter
4 Grade
Adding and Subtracting
Equivalent Fractions
Divisibility by 2, 3, 4, 5, 9
Area of Squares and Rectangles
Fractions
Equivalent Fractions
Least Common Multiple
Adding and Subtracting
Fraction Multiplication and Division
Operations
Mixed Numbers
Decimals
6 Grade
Percents
Signed Numbers
The Coordinate Plane
Equations
Polynomials
Symplifying Expressions
Polynomial Expressions
Factoring
7 Grade
Angles
Parametric Linear Equations
Word Problems
Exponentiation
Roots
Quadratic Equations
Vieta's Formulas
Progressions
Arithmetic Progressions
Geometric Progression
Progressions
Number Sequences
Reciprocal Equations
Logarithms
Logarithmic Expressions
Logarithmic Equations
Extremal value problems
Trigonometry
Geometry
Intercept Theorem
Law of Sines
Law of Cosines
Probability
Limits of Functions
Properties of Triangles
Pythagorean Theorem
Inverse Trigonometric Functions
Analytic Geometry
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
Submit a problem on this page.
Problem text:
Solution:
Answer:
Your name(if you would like to be published):
E-mail(you will be notified when the problem is published)
Notes
: use [tex][/tex] (as in the forum if you would like to use latex).
Correct:
Wrong:
Solution seen:
Contact email:
Follow us on
Twitter
Google+
Facebook
Author
Copyright © 2005-2015.