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A circle is drawn centered on the midpoint of the line segment OP, having diameter OP, where O is again the center of the circle C. 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.
where a is the radius of the circle, (,) are the polar coordinates of a generic point on the circle, and (,) are the polar coordinates of the centre of the circle (i.e., r 0 is the distance from the origin to the centre of the circle, and φ is the anticlockwise angle from the positive x axis to the line connecting the origin to the centre of ...
h = the height of the semi-ellipsoid from the base cicle's center to the edge Solid paraboloid of revolution around z-axis: a = the radius of the base circle h = the height of the paboloid from the base cicle's center to the edge
A tangential polygon has each of its sides tangent to a particular circle, called the incircle or inscribed circle. The centre of the incircle, called the incentre, can be considered a centre of the polygon. A cyclic polygon has each of its vertices on a particular circle, called the circumcircle or circumscribed circle. The centre of the ...
In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure. [further explanation needed] The same definition extends to any object in -dimensional Euclidean space. [1]
The general equation for a circle with a center at (,) and radius a is + =. This can be simplified in various ways, to conform to more specific cases, such as the equation r ( φ ) = a {\displaystyle r(\varphi )=a} for a circle with a center at the pole and radius a .
These points are located at the intersection of the circle with the vertical line passing through the center of the circle, . Thus, the magnitude of the maximum and minimum shear stresses are equal to the value of the circle's radius R {\displaystyle R}
This circle, which is the one among all tangent circles at the given point that approaches the curve most tightly, was named circulus osculans (Latin for "kissing circle") by Leibniz. The center and radius of the osculating circle at a given point are called center of curvature and radius of curvature of the curve at that