midcircle

1. not comparableIn, at, or towards the middle of a circle.

   The goalkeeper who is initially positioned midcircle defends the goal.

   2005, Claire Mitchell-Taverner, Field Hockey Techniques & Tactics, page 91

plural midcircles

1. A circle that is in the middle.

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

   2012, Rhonda L. Clements, Amy Meltzer Rady, Urban Physical Education, page 55

2. The middle of a circle.

   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.

   1993, Philosophical Inquiry, volumes 15-16, page 52

3. The middle of an act of circling.

   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.

   2001, Steve Earle, “Jaguar Dance”, in Doghouse Roses: Stories, page 60

4. spherical geometryThe great circle that is equidistant from two poles.

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

   1790, Charles Wildbore, “On Spherical Motion”, in Philosophical Transactions of the Royal Society of London, Volume LXXX, Part 1, page 551

5. inversive geometryA reference generalised circle through which two given circles are inverses of each other.

   1 more example

   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.

   1994, Tim Gallagher, Bruce Piper, “Chapter 7: Convexity Preserving Surface Interpolation”, in Nickolas S. Sapidis, editor, Designing Fair Curves and Surfaces, page 179

   Synonyms: circle of antisimilitude

6. geometryThe circle (if one exists) that passes through the midpoint of each side of a given polygon, especially a triangle.

   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.

   2010, Alex Bellos, Here's Looking at Euclid, page 61