Search results
Results From The WOW.Com Content Network
The same reciprocal relation exists between a point P outside the circle and the secant line joining its two points of tangency. If a point P is exterior to a circle with center O, and if the tangent lines from P touch the circle at points T and S, then ∠TPS and ∠TOS are supplementary (sum to 180°).
compute the angle difference α − β = Δ; use that to calculate β = (180° − γ − Δ)/2 and then α = β + Δ. Once an angle opposite a known side is computed, the remaining side c can be computed using the law of sines .
Tangent to a curve. The red line is tangential to the curve at the point marked by a red dot. Tangent plane to a sphere. In geometry, the tangent line (or simply tangent) to a plane curve at a given point is, intuitively, the straight line that "just touches" the curve at that point.
The inclination, sometimes called inversive distance, is when the circles are tangent and oriented the same way at their point of tangency, when the two circles are tangent and oriented oppositely at the point of tangency, for orthogonal circles, outside the interval [,] for non-intersecting circles, and in the limit as one circle degenerates ...
2 The number of lines meeting 4 general lines in space; 8 The number of circles tangent to 3 general circles (the problem of Apollonius). 27 The number of lines on a smooth cubic surface (Salmon and Cayley) 2875 The number of lines on a general quintic threefold; 3264 The number of conics tangent to 5 plane conics in general position
Being tangent to five given lines also determines a conic, by projective duality, but from the algebraic point of view tangency to a line is a quadratic constraint, so naive dimension counting yields 2 5 = 32 conics tangent to five given lines, of which 31 must be ascribed to degenerate conics, as described in fudge factors in enumerative ...
If the degree of the curve is d then the degree of the polar is d − 1 and so the number of tangents that can be drawn through the given point is at most d(d − 1). The dual of a line (a curve of degree 1) is an exception to this and is taken to be a point in the dual space (namely the original line).
One needs a definition of intersection number in order to state results like Bézout's theorem. The intersection number is obvious in certain cases, such as the intersection of the x- and y-axes in a plane, which should be one. The complexity enters when calculating intersections at points of tangency, and intersections which are not just ...