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By Thales' theorem, any triangle inscribed in a semicircle with a vertex at each of the endpoints of the semicircle and the third vertex elsewhere on the semicircle is a right triangle, with a right angle at the third vertex. All lines intersecting the semicircle perpendicularly are concurrent at the center of the circle containing the given ...
The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane.
Regular polygons; Description Figure Second moment of area Comment A filled regular (equiliteral) triangle with a side length of a = = [6] The result is valid for both a horizontal and a vertical axis through the centroid, and therefore is also valid for an axis with arbitrary direction that passes through the origin.
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, ... Upper semicircle with radius 1 and center (0, 0) ...
The Wigner semicircle distribution, named after the physicist Eugene Wigner, is the probability distribution defined on the domain [−R, R] whose probability density function f is a scaled semicircle, i.e. a semi-ellipse, centered at (0, 0):
The intersection points T 1 and T 2 of the circle C and the new circle are the tangent points for lines passing through P, by the following argument (tan). The line segments OT 1 and OT 2 are radii of the circle C; since both are inscribed in a semicircle, they are perpendicular to the line segments PT 1 and PT 2, respectively. But only a ...
Semicircle, a geometric shape that forms half of a circle Topics referred to by the same term This disambiguation page lists articles associated with the title Hemicircle .
The moment of inertia for a semicircle, best expressed in cylindrical coordinates, is = (,,). Solving the integral, one finds that the moment of inertia of a semicircle is I = m s 2 {\displaystyle I=ms^{2}} , exactly the same for a hoop of the same radius.