Lengths of Sides and Angle Bisectors Are Rational Together

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Let , , be rational numbers and define a triangle by the lengths of its sides:





which are scaled by their greatest common divisor to be integers.

Let be the incenter of and let , , be the feet of the corresponding Cevians.

Then the lengths of , , are rational.

Conversely, if the lengths of the Cevians are rational, so are the lengths of the triangle.


Contributed by: Minh Trinh Xuan (August 2022)
Open content licensed under CC BY-NC-SA



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.