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The polar triangle is a geometric figure formed by connecting the poles of a spherical triangle to the vertices of that triangle. In spherical geometry, if a triangle is defined by three points on the surface of a sphere, the polar triangle consists of the points that are the poles of the arcs connecting these vertices. This concept is useful in various applications of spherical trigonometry, particularly in navigation and astronomy, where understanding the relationships between angles and distances on a sphere is crucial. The relationships between the angles and sides of the polar triangle can be derived from those of the original spherical triangle.

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1mo ago

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