A Parallelogram Defined by the Centers of Four Circumcircles

Requires a Wolfram Notebook System

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

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Let ABC be a triangle. Let the line DE be parallel to AC with D on AB and E on BC. Let the line GH be parallel to AB with H on AC and G on BC. Let F be the intersection of DE and GH. Let O, , , and be the circumcircles of the triangles ABC, DBE, FEG, and CGH, respectively. Then is a parallelogram.

Contributed by: Jay Warendorff (March 2011)
After work by: Antonio Gutierrez
Open content licensed under CC BY-NC-SA


Snapshots


Details

The statement of the theorem is in Problem 93. Similar Triangles, Circumcircles, Parallelogram.



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