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Results tagged with plane-geometry
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user 265714
Plane Geometry is about flat shapes like lines, circles and triangles , shapes that can be drawn on a piece of paper
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Radical line of two ellipses
The equation of an ellipse with focal points $(a_1,b_1)$ and $(a_2,b_2)$ which passes through the point $(a_3,b_3)$ is given by the equation
$$\begin{gathered}
\sqrt{ (x-a_1)^2+(y-b_1)^2 } + \sqrt{ (x …
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Coordinates of the centers of the insphere and circumsphere
Suppose we are working in $\mathbb{R}^3$ space and we have four non-coplanar and non-collinear points, $(x_a, y_a, z_a)$, $(x_b, y_b, z_b)$, $(x_c,y_c, z_c)$, and $(x_d, y_d, z_d)$. How does one deter …
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Twin circles in a quadrilateral
The circumcenters of the four triangles of a complete quadrilateral along with the two points of completion form two congruent circles (in black).
Surely this must've been done before - what's the fo …
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A certain circle formed by perpendiculars
If six points are chosen, two points on each side of a triangle, such that they have the same ratio of distances to vertices, then the perpendicular lines through those points meet at six concyclic p …
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