1, chord length = 2Sina
R is the radius and a is the central angle.
2. arc length l and radius r.
Chord length =2Rsin(L* 180/πR)
A formula for finding chord length d when a straight line intersects a conic curve.
Chord length = │ x1-x2 │√ (k2+1) = │ y1-y2 │√ [(1/k2)+1].
Where k is the slope of a straight line, (x 1, y 1), (x2, y2) is the intersection of a straight line and a curve, "│ │" is the absolute value symbol, and "√" is the root sign.
PS: Conic curves are some curves obtained by cutting a cone flat (strictly speaking, a right conical surface is completely tangent to a plane) in mathematics and geometry, such as ellipse, hyperbola, parabola and so on.
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 of the intersection of a straight line and a curve. However, compared with this method, it is a bit complicated to solve the chord length of the over-focus conic curve, and it is simpler to derive the formula of the focal chord length of various curves by using the definition of conic curve and related theorems.
d =？
When we know the chord length of the circular equation and the linear equation, we can substitute the linear equation into the circular equation to eliminate the unknowns, and get a quadratic equation with one variable, where △ is b 2-4ac in the quadratic equation with one variable and A is the quadratic coefficient.
Appendix:
Equation 2 conforms to an elliptic conic curve, not just a circle. Vieta's theorem, x 1+x2=-b/a, x 1x2=c/a, and then divide. Pythagorean theorem can also be used when we know the chord length of circle and straight line equations. (Distance from point to line, radius, half chord)
References:
Baidu encyclopedia-chord length formula