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
Addition and Subtraction within 20
2 Grade
Adding and Subtracting up to 100
Addition and Subtraction within 20
3 Grade
Addition and Subtraction within 1000
Multiplication up to 5
Multiplication Table
Dividing
Rounding
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
Expressions
6 Grade
Percents
Signed Numbers
The Coordinate Plane
Equations
Expressions
Polynomials
Polynomial Vocabulary
Symplifying Expressions
Polynomial Expressions
Factoring
7 Grade
Angles
Linear Functions
8 Grade
Linear Functions
Systems of equations
Slope
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
Numbers Classification
Geometry
Intercept Theorem
Slope
Law of Sines
Law of Cosines
Vectors
Analytic Geometry
Probability
Limits of Functions
Properties of Triangles
Pythagorean Theorem
Matrices
Inverse Trigonometric Functions
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:
Unsolved problems:
Contact email:
Follow us on
Twitter
Facebook
Author
Copyright © 2005 - 2019.