Inequality for a Cevian Involving the Circumradius

Let be a triangle; define , , and let be the circumcircle of .
For a point , let , , be signed areas and set , the barycentric coordinates of , so that .
Let .
Then , with equality if and only if is on .
You can drag the vertices , , .

SNAPSHOTS

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