11403

# Three Coplanar Bisectors in Unit Sphere Construction

Draw a spherical triangle on the surface of the unit sphere centered at . Let be the point opposite on . Let the sides opposite the corresponding vertices be the arcs , , . Then the bisectors of , and (the supplementary angle of ) lie in the same plane.

### DETAILS

Vectors parallel to the bisectors of , , are , , , but , so the vectors are coplanar [3, p. 83].
References
[1] Wikipedia. "Spherical Law of Cosines." (May 15, 2017) en.wikipedia.org/wiki/Spherical_law_of _cosines.
[2] Wikipedia. "Spherical Trigonometry." (May 15, 2017) en.wikipedia.org/wiki/Spherical_trigonometry.
[3] V. V. Prasolov and I. F. Sharygin, Problems in Stereometry (in Russian), Moscow: Nauka, 1989.

### 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.