10217

# Triangle Area Bisectors

Area bisectors are straight lines that divide a triangle into two parts of equal area. They are all tangent lines to three different hyperbolas whose asymptotes are the straight lines containing the sides of the triangle. This Demonstration shows the bisectors and the hyperbolas for any triangle. For any fraction of the total area , there are two lines emanating from each vertex that divide the triangle into a part with of the total area and a part with of the total area. These six lines are tangent to six hyperbolas, and this scenario can be viewed by controlling the value of with the top slider.

### DETAILS

For the standard case of 1:1 ratio an interesting problem is the following: given some triangle, what is the probability for an arbitrary point in the interior of the triangle to belong to exactly different area bisectors? The probability for is 0. The probability for is the same for all triangles and is less than 2%.
When the three hyperbolas are tangent, the points of tangency are the midpoints of the medians.

### PERMANENT CITATION

 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 » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.