# Distance between Orthocenter and Center of Taylor Circle

Initializing live version

Requires a Wolfram Notebook System

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

Given a triangle , let , , be the feet of the perpendiculars to the sides opposite , , . (These perpendiculars are the altitudes, drawn dashed red; they intersect at the orthocenter .) Draw two perpendiculars each from , , to the sides of to get six green points. These six points are concyclic, defining the Taylor circle with Kimberling center [1].

[more]

Let , , be the side lengths of , let be the circumradius of and let be the Brocard angle of .

Define

,

,

.

Then

.

You can drag the vertices , and .

[less]

Contributed by: Minh Trinh Xuan (August 2022)
Open content licensed under CC BY-NC-SA

## Details

Reference

[1] C. Kimberling. "Encyclopedia of Triangle Centers." (Aug 2, 2022) faculty.evansville.edu/ck6/encyclopedia.

## Permanent Citation

Minh Trinh Xuan

 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