Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
9. If three lines whose equations are
y
=
m
1
x
+
c
1
,
y
=
m
2
x
+
c
2
y=m_{1} x+c_{1}, y=m_{2} x+c_{2}
y
=
m
1
x
+
c
1
,
y
=
m
2
x
+
c
2
and
y
=
m
3
x
+
c
3
y=m_{3} x+c_{3}
y
=
m
3
x
+
c
3
are concurrent, then show that
m
1
(
c
2
−
c
3
)
+
m
2
(
c
3
−
c
1
)
+
m
3
(
c
1
−
c
2
)
=
0
m_{1}\left(\mathrm{c}_{2}-\mathrm{c}_{3}\right)+m_{2}\left(\mathrm{c}_{3}-\mathrm{c}_{1}\right)+m_{3}\left(\mathrm{c}_{1}-\mathrm{c}_{2}\right)=0
m
1
(
c
2
−
c
3
)
+
m
2
(
c
3
−
c
1
)
+
m
3
(
c
1
−
c
2
)
=
0
.
Browse the problem library