The Plemelj Construction of a Triangle: 6

This Demonstration constructs a triangle given the length of its base, the length of the altitude from to and the difference between the angles at and .
Step 1: Draw a vertical segment of length . Draw two horizontal rays and from and , respectively. From , draw a ray at angle with respect to the ray . Let be the intersection of the rays and .
Step 2: Draw a segment of length perpendicular to the ray .
Step 3: Draw a circle with center and radius . The ray intersects the circle at and .
Step 4: On , draw the point so that . On , measure out the point so that .
Step 5: The triangle satisfies the stated conditions.
Draw the circumcircle of the triangle with center . Let the point be the foot of the altitude from . Then . By construction, the power of the point with respect to is , so by Euclid III.37 [1, pp. 15], is tangent to and as angles with orthogonal legs. So .


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


For the history of this problem, references and a photograph of Plemelj's first solution, see The Plemelj Construction of a Triangle: 1.
[1] G. E. Martin, Geometric Constructions, Springer, New York, 1998.
    • 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.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+