Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Show that the circumcircle of the triangle formed by the lines
a
x
+
b
y
+
c
=
0
ax + by + c = 0
a
x
+
b
y
+
c
=
0
;
b
x
+
c
y
+
a
=
0
bx + cy + a = 0
b
x
+
cy
+
a
=
0
and
c
x
+
a
y
+
b
=
0
cx + ay + b = 0
c
x
+
a
y
+
b
=
0
passes through the origin if
(
b
2
+
c
2
)
(
c
2
+
a
2
)
(
a
2
+
b
2
)
=
a
b
c
(
b
+
c
)
(
c
+
a
)
(
a
+
b
)
(b^2 + c^2)(c^2 + a^2)(a^2 + b^2) = abc(b + c)(c + a)(a + b)
(
b
2
+
c
2
)
(
c
2
+
a
2
)
(
a
2
+
b
2
)
=
ab
c
(
b
+
c
)
(
c
+
a
)
(
a
+
b
)
.
Browse the problem library