Let the radius of a circle be r and the center of the circle be (m, n).
The linear equation is ax+by+c=0.
The distance between chord centers is d.
Then d 2 = (ma+nb+c) 2/(a 2+b 2)
Then the square of half the chord length is (r 2-d 2)/2.
Chord length formula, here refers to the formula of chord length d obtained by intersection of straight line and conic curve.
Conic curves are some curves obtained by cutting a cone flat in mathematics and geometry (strictly speaking, a right conical surface is completely tangent to a plane), such as ellipse, hyperbola and parabola.
Extended data:
The positional relationship between straight line and conic curve is one of the important contents of plane analytic geometry, and it is also a hot spot in college entrance examination. The main contents of the survey include: the common points of straight lines and conic curves; Related problems of strings (chord length, midpoint chord, verticality, fixed score point, etc.). ); Symmetry problem; Extreme value problem, trajectory problem, standard equation problem of conic curve, etc.
The thinking method of setting without seeking is very effective for finding the chord length of the intersection point between a straight line and a curve. However, compared with this method, it is a bit complicated to find the chord length of the conic curve that has passed the focus, and it is simpler to derive the formula of the chord length of the focus of various curves by using the definition of conic curve and related theorems.