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Complete works of chord length formulas of circles
The formula of the chord length of a circle is: AB=|x 1-x2|√( 1+k? )= | y 1-y2 | √( 1+ 1/k? )。

Chord length is the length of a line segment connecting any two points on a circle; Chord length formula, here refers to the chord length formula obtained by the 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 general method to find the chord length when a straight line intersects a conic curve is to substitute the straight line y=kx+b into the curve equation, turn it into a quadratic equation about x (or about y), set the coordinates of the intersection point, and use Vieta's theorem and chord length formula to find the chord length. This thinking method of substituting the whole, setting without seeking is very effective for finding the chord length when a straight line intersects a curve.

However, compared with this method, it is a bit complicated to solve the chord length of over-focused conic curve, and it is simpler to derive the chord length formulas of various curves by using the definition of conic curve and related theorems.

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