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Any two polar circles of two triangles in an orthocentric system are orthogonal. [1]: p. 177 The polar circles of the triangles of a complete quadrilateral form a coaxal system. [1]: p. 179 The most important property of the polar circle is the triangle is self-polar; the polar of each side/point is the opposite side/point.
The polar triangle A'B'C' The polar triangle associated with a triangle ABC is defined as follows. Consider the great circle that contains the side BC. This great circle is defined by the intersection of a diametral plane with the surface.
If two lines a and k pass through a single point Q, then the polar q of Q joins the poles A and K of the lines a and k, respectively. The concepts of a pole and its polar line were advanced in projective geometry. For instance, the polar line can be viewed as the set of projective harmonic conjugates of a given point, the pole, with respect to ...
Pages in category "Circles defined for a triangle" The following 15 pages are in this category, out of 15 total. ... Polar circle (geometry) S.
The sum of the angles of a spherical triangle is not equal to 180°. A sphere is a curved surface, but locally the laws of the flat (planar) Euclidean geometry are good approximations. In a small triangle on the face of the earth, the sum of the angles is only slightly more than 180 degrees. A sphere with a spherical triangle on it.
It can be shown that K is the perspector [5] of E, namely, where ABC and the polar triangle [6] with respect to E are perspective. The polar triangle is bounded by the tangents to E at the vertices of ABC. For example, the Trilinear polar of a point on the circumcircle must pass through its perspector, the Symmedian point X(6).