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First generalization: Let ABC be a triangle, P be a point on the plane, let three parallel segments AA', BB', CC' such that its midpoints and P are collinear. Then PA', PB', PC' meet BC, CA, AB respectively at three collinear points. [6] Dao's second generalization. Second generalization: Let a conic S and a point P on the plane.
Ordinary trigonometry studies triangles in the Euclidean plane .There are a number of ways of defining the ordinary Euclidean geometric trigonometric functions on real numbers, for example right-angled triangle definitions, unit circle definitions, series definitions [broken anchor], definitions via differential equations [broken anchor], and definitions using functional equations.
The Simson line of a vertex of the triangle is the altitude of the triangle dropped from that vertex, and the Simson line of the point diametrically opposite to the vertex is the side of the triangle opposite to that vertex. If P and Q are points on the circumcircle, then the angle between the Simson lines of P and Q is half the angle of the ...
Fig. 1 – A triangle. The angles α (or A), β (or B), and γ (or C) are respectively opposite the sides a, b, and c.. In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles.
Each face (orange grid) is Pascal's 2-simplex (Pascal's triangle). Arrows show derivation of two example terms. Arrows show derivation of two example terms. In mathematics , Pascal's simplex is a generalisation of Pascal's triangle into arbitrary number of dimensions , based on the multinomial theorem .
After nearly derailing a spending bill and forcing a government shutdown last month, President-elect Donald Trump continues to shake up legislative business on Capitol Hill, offering shifting ...
Let ABC be any triangle. Let the Euler line of triangle ABC meet the sidelines BC, CA and AB of triangle ABC at D, E and F respectively. Let A g B g C g be the triangle formed by the Euler lines of the triangles AEF, BFD and CDE, the vertex A g being the intersection of the Euler lines of the triangles BFD and CDE, and similarly for the other two vertices.
Average mortgage rates increase higher as of Tuesday, January 14, 2025, pushing the 30-year fixed benchmark to its highest levels since May following last week's stronger-than-expected jobs report.