 # 19. Construct a Triangle Given the Length of Its Base, the Difference of Its Base Angles and a Special Point of Intersection

Initializing live version 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 difference of the base angles and the point , the intersection of and , where is the circumcenter.

[more]

Construction

Step 1: Draw a segment of length and a point on between and . Let be the midpoint of .

Step 2: Let be the intersection of the perpendicular bisector of and the ray through that forms the angle with .

Step 3: Draw a circle with center and radius . Let be the intersection of and .

Step 4: Triangle is a solution of the problem.

Verification

The circle is the circumcircle of triangle , so .

[less]

Contributed by: Izidor Hafner (October 2017)
Open content licensed under CC BY-NC-SA

## Snapshots   ## Details

Reference

 D. S. Modic, Triangles, Constructions, Algebraic Solutions (in Slovenian), Ljubljana: Math Publishers, 2009.

## Permanent Citation

Izidor Hafner

 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. Send