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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.
Moreover, the circumcenter, the Lemoine point, and the first two Brocard points are concyclic—they all fall on the same circle, of which the segment connecting the circumcenter and the Lemoine point is a diameter.
The Brocard triangle (in black) of the triangle ABC. B1 and B2 are the two Brocard points.. In geometry, the Brocard triangle of a triangle is a triangle formed by the intersection of lines from a vertex to its corresponding Brocard point and a line from another vertex to its corresponding Brocard point and the other two points constructed using different combinations of vertices and Brocard ...
In the early days, the expression "new triangle geometry" referred to only the set of interesting objects associated with a triangle like the Lemoine point, Lemoine circle, Brocard circle and the Lemoine line. Later the theory of correspondences which was an offshoot of the theory of geometric transformations was developed to give coherence to ...
The circle with OK as diameter is the Brocard circle of triangle ABC. The line through O perpendicular to the line BC intersects the Brocard circle at another point A'. The line through O perpendicular to the line CA intersects the Brocard circle at another point B'.
Barnard's Star is a small red dwarf star in the constellation of Ophiuchus. At a distance of 5.96 light-years (1.83 pc ) from Earth, it is the fourth-nearest-known individual star to the Sun after the three components of the Alpha Centauri system, and is the closest star in the northern celestial hemisphere . [ 15 ]
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".