The Plemelj Construction of a Triangle: 13

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration constructs a triangle given the length of its base , the length of the altitude from to and the difference between the angles and at and . This is not one of Plemelj's original constructions, but a new one based on his equation , where and . It is the same as The Plemelj Construction of a Triangle: 8, but the verification is different.


The modified equation is .


Step 1: Draw a straight line of length and a line parallel to at distance . Let be the midpoint of , and let be the point on directly above . Let be the reflection of in .

Step 2: Draw a circle with center and radius .

Step 3: Draw the ray from at the angle from to intersect at the point .

Step 4: Draw the circle with center and radius .

Step 5: Measure out a point on the circle at distance from .

Step 6: The point is the intersection of and the right bisector of .

Step 7: The triangle meets the stated conditions.


Angle , so . But , since .

So . Since , .


Contributed by: Izidor Hafner, Nada Razpet and Marko Razpet (September 2017)
Open content licensed under CC BY-NC-SA



For the history of this problem, references and a photograph of Plemelj's first solution, see The Plemelj Construction of a Triangle: 1.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.