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398:. These five points, together with the other two points on the circle (the circumcenter and symmedian), justify the name "seven-point circle".
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50:
of the triangle, and is centered at the midpoint of the line segment joining them (so that this segment is a
417:, the circumcenter and symmedian coincide and therefore the Brocard circle reduces to a single point.
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183:-coordinate of a point is the area of the triangle made by that point with the side of length
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429:, who presented a paper on it to the French Association for the Advancement of Science in
375:{\displaystyle b^{2}c^{2}x^{2}+a^{2}c^{2}y^{2}+a^{2}b^{2}z^{2}-a^{4}yz-b^{4}xz-c^{4}xy=0.}
47:
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527:, New Mathematical Library, vol. 37, Cambridge University Press, p. 110,
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203:, etc), the Brocard circle consists of the points satisfying the equation
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27:
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503:
A history of elementary mathematics: with hints on methods of teaching
39:
590:
452:"Circles and triangle centers associated with the Lucas circles"
524:
Episodes in
Nineteenth and Twentieth Century Euclidean Geometry
18:
575:(1953), "Henri Brocard and the geometry of the triangle",
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derived from a given triangle. It passes through the
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394:lie on this circle, as do the vertices of the
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552:(5th ed.), Brooks/Cole, p. 184,
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163:for points inside the triangle (where the
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623:MacTutor History of Mathematics Archive
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7:
506:, The Macmillan company, p. 261
16:Circle constructed from a triangle
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425:The Brocard circle is named for
122:of the given triangle, and the
685:Circles defined for a triangle
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132:
1:
62:In terms of the side lengths
450:Moses, Peter J. C. (2005),
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628:University of St Andrews
578:The Mathematical Gazette
548:Smart, James R. (1997),
156:{\displaystyle (x,y,z)}
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614:Robertson, Edmund F.
403:first Lemoine circle
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612:O'Connor, John J.;
459:Forum Geometricorum
413:If the triangle is
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36:seven-point circle
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670:Nine-point circle
573:Guggenbuhl, Laura
550:Modern Geometries
196:{\displaystyle a}
176:{\displaystyle x}
124:areal coordinates
115:{\displaystyle c}
95:{\displaystyle b}
75:{\displaystyle a}
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649:"Brocard Circle"
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585:(322): 241–243,
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519:Honsberger, Ross
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618:"Henri Brocard"
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591:10.2307/3610034
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48:symmedian point
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32:Brocard circle
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559:0-534-35188-3
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534:9780883856390
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480:on 2018-04-22
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428:
427:Henri Brocard
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409:Special cases
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21:
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492:
482:, retrieved
475:the original
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412:
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389:
61:
44:circumcenter
35:
31:
25:
415:equilateral
484:2019-01-05
465:: 97–106,
437:References
654:MathWorld
433:in 1881.
348:−
329:−
310:−
679:Category
664:See also
521:(1995),
500:(1917),
390:The two
58:Equation
52:diameter
28:geometry
599:3610034
471:2195737
431:Algiers
421:History
38:) is a
597:
556:
531:
469:
102:, and
40:circle
30:, the
595:JSTOR
478:(PDF)
455:(PDF)
554:ISBN
529:ISBN
46:and
34:(or
587:doi
54:).
26:In
681::
651:.
626:,
620:,
616:,
593:,
583:37
581:,
467:MR
461:,
457:,
405:.
370:0.
82:,
657:.
602:.
589::
538:.
508:.
463:5
367:=
364:y
361:x
356:4
352:c
345:z
342:x
337:4
333:b
326:z
323:y
318:4
314:a
305:2
301:z
295:2
291:b
285:2
281:a
277:+
272:2
268:y
262:2
258:c
252:2
248:a
244:+
239:2
235:x
229:2
225:c
219:2
215:b
191:a
171:x
151:)
148:z
145:,
142:y
139:,
136:x
133:(
110:c
90:b
70:a
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