The circle is named after H.M.Taylor (18421927) who discussed
it in 1883.
Reference: The Relations of the
Intersections of a Circles with a Triangle, HM Taylor 
Proceedings of the London Mathematical Society, 1883.
Dynamic Geometry: You can alter the figure above
dynamically in order to test and prove (or disproved)
conjectures and gain mathematical insight that is less
readily available with static drawings by hand.
This page uses the
TracenPoche
dynamic geometry software and requires
Adobe Flash player 7 or higher.
TracenPoche is a project of Sesamath, an association of French
teachers of mathematics.
Instruction to explore the
illustration above:

Animation. Click the red
button
to start/stop animation

Manipulate. Drag points A
and C to change the figure.

Step by Step construction.
Press P and click the left mouse
button
on any free area to show the
stepbystep bar and start the
construction:
Hide the stepbystep bar by
using again the combination P +
click left mouse button.
Henry Martyn Taylor and the blind student of mathematics
"One Braille notation was devised by the eminent Cambridge
mathematician, Henry Martyn Taylor, who was overtaken by
blindness in 1894, when engaged in the preparation of an
edition of Euclid for the Cambridge University Press. By
means of his ingenious and well thought out Braille notation
he was enabled to transcribe many advanced scientific and
mathematical works, and in 1917, with the assistance of Mr.
Emblen, a blind member of the staff of the National
Institute for the Blind, he perfected it. It was recognised
as so comprehensive that it was soon adopted as the standard
mathematical and chemical notation, and is universally used
by Englishspeaking people." Taken from: NEW BEACON, Vol.
XVIII, No. 210, June 15, 1934, pp. 146148
