midcircle

English

Two (tan) midcircles (circles through which given circles are inverse) of noncongruent intersecting circles (black)

Etymology

From mid- +‎ circle.

Adverb

midcircle (not comparable)

1. In, at, or towards the middle of a circle.
   • 2005, Claire Mitchell-Taverner, Field Hockey Techniques & Tactics, page 91:

     The goalkeeper who is initially positioned midcircle defends the goal.

Noun

midcircle (plural midcircles)

1. A circle that is in the middle.
   • 2012, Rhonda L. Clements, Amy Meltzer Rady, Urban Physical Education, page 55:

     Play begins when the teacher bounces a basketball on the floor in the center of the midcircle.

2. The middle of a circle.
   • 1993, Philosophical Inquiry, volumes 15-16, page 52:

     As the picturing of reality by the arts and sciences progresses, the innermost circle approaches the midcircle. But the midcircle, regardless of the extent of its expansion, will never coincide with the outer circle.

3. The middle of an act of circling.
   • 2001, Steve Earle, “Jaguar Dance”, in Doghouse Roses: Stories, page 60:

     The upstart had stopped in midcircle and suddenly lunged at the veteran, and as he closed in, the veteran could smell both liquor and fear on his breath, which came in short, desperate gasps.

4. (spherical geometry) The great circle that is equidistant from two poles.
   • 1790, Charles Wildbore, “On Spherical Motion”, in Philosophical Transactions of the Royal Society of London, Volume LXXX, Part 1, page 551:

     But, though there is no perturbating motive force in the direction of the midcircle, there is nevertheleſs an accelerative one acting along it; […] .

5. (inversive geometry) A reference generalised circle through which two given circles are inverses of each other.
   • 1994, Tim Gallagher, Bruce Piper, “Chapter 7: Convexity Preserving Surface Interpolation”, in Nickolas S. Sapidis, editor, Designing Fair Curves and Surfaces, page 179:

     For any two circles (spheres) there always exists at least one midcircle (midsphere) which inverts the two given circles (spheres) into each other. in the older literature this is also known as the circle (sphere) of antisimilitude. […] The center of a midcircle (midsphere) is the center of similitude of two given circles (spheres). […] Clearly the midcircle (midsphere) of two equal circles (spheres) is the midline (midplane) between the two, which is partial justification for calling inversion in a circle or sphere reflection in a circle or sphere.

6. (geometry) The circle (if one exists) that passes through the midpoint of each side of a given polygon, especially a triangle.
   • 2010, Alex Bellos, Here's Looking at Euclid, page 61:

     Every triangle has a midcircle, and its center is the fourth kind of middle point that a triangle can have. In 1767 Leonhard Euler proved that for all triangles, the orthocenter, the circumcenter, the centroid and the center of the midcircle are always on the same line.

Synonyms

• (circle through which two given circles are inverses of each other): circle of antisimilitude

Related terms

• midsphere