12,000+ Interactive Demonstrations Powered by Notebook Technology »

Lengths of Sides and Angle Bisectors Are Rational Together

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.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

RELATED LINKS

PERMANENT CITATION

 Minh Trinh Xuan
"Lengths of Sides and Angle Bisectors Are Rational Together"
 http://demonstrations.wolfram.com/LengthsOfSidesAndAngleBisectorsAreRationalTogether/
 Wolfram Demonstrations Project
 Published: June 15, 2022
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.





Related Topics