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In geometry, the Brocard circle (or seven-point circle) is a circle derived from a given triangle. It passes through the circumcenter and symmedian point of the triangle, and is centered at the midpoint of the line segment joining them (so that this segment is a diameter ).
Brocard's most well-known contributions to mathematics are the Brocard points, the Brocard circle, and the Brocard triangle. The positive Brocard point (sometimes known as the first Brocard point) of a Euclidean plane triangle is the interior point of the triangle for which the three angles formed by two of the vertices and the point are equal.
The Zodiac is an ancient circle of stars [11] where some stars are symbolically combined into 12 star signs also known as constellations. The etymology of the term Zodiac comes from the Latin zōdiacus, from the Greek ζῳδιακός [κύκλος], meaning "[circle] of animals", derived from ζῴδιον, the diminutive of ζῷον "animal".
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The Brocard points are an example of a bicentric pair of points, but they are not triangle centers because neither Brocard point is invariant under similarity transformations: reflecting a scalene triangle, a special case of a similarity, turns one Brocard point into the other.
Brocard can refer to: Brocard (law) Henri Brocard, a nineteenth-century mathematician, and these geometrical entities he discovered: Brocard points; Brocard triangle; Brocard circle; Saint Brocard, first of the priors of the Carmelite Order according to oral tradition
The Crown of Immortality, held by the allegorical figure Eterna (Eternity) on the Swedish House of Knights fresco by David Klöcker Ehrenstrahl. The Crown of Immortality is a literary and religious metaphor traditionally represented in art first as a laurel wreath and later as a symbolic circle of stars (often a crown, tiara, halo or aureola).
Star of Ishtar, an ancient symbol associated with the Mesopotamian goddess Ishtar; Star and crescent, an Islamic symbol; The Star (Tarot card), one of the Major Arcana; Druze star, a symbol of the Druze religion; Marian star, a six-pointed star used as a Roman Catholic symbol of celestial objects; Rub el Hizb, a common Islamic symbol