Rational Isogonal Conjugates

​
generating rationals:
a
-3
b
-
7
6
Hover over a vertex to see its coordinates. Hover over a line segment to see its length.
Given a triangle
ABC
, draw lines from the vertices to an arbitrary point
X
. Reflect those three lines in the angle bisectors (shown in red). The three new lines intersect in a point
X
called the isogonal conjugate of
X
.
If a triangle
Δ
has three rational sides, it is called a basic rational triangle. A point
P
is called a rational point of the rational triangle
Δ
if the distance from
P
to the vertices of
Δ
is also rational.
It is a theorem that
X
is a rational point of
Δ
if and only if
X
is a rational point of
Δ
.
In this Demonstration, rational values
a
and
b
are used to generate a pair of rational isogonal conjugates
X
and
X
in a rational triangle
ABC
.

External Links

Angle Bisector (Wolfram MathWorld)
Isogonal Conjugate (Wolfram MathWorld)

Permanent Citation

Minh Trinh Xuan
​
​"Rational Isogonal Conjugates"​
​http://demonstrations.wolfram.com/RationalIsogonalConjugates/​
​Wolfram Demonstrations Project​
​Published: January 1, 1999