已知弧长拱高弦长求半径 知道弦长和拱高,怎么求半径,

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R^2=(R-H)^2+(L/2)^2
R^2=R^2-2*R*H+H^2+L^2/4
2*R*H=H^2+L^2/4
R=H/2+L^2/(8*H)
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\u5f26\u957f|AB|=\u221a[\uff08x1-x2\uff09^2+(y1-y2)^2]=\u221a[(x1-x2)^2+(kx1-kx2)^2]=\u221a\uff081+k^2\uff09|x1-x2|=\u221a(1+k^2)\u221a[\uff08x1+x2\uff09^2-4x1x2]

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\u5df2\u77e5\u5f26\u957fL\u548c\u62f1\u9ad8H\u6c42\u534a\u5f84R\u7684\u516c\u5f0f\uff1aR^2=(R-H)^2+(L/2)^2
2.\u89e3\u9898\u6b65\u9aa4\uff1a
R^2=(R-H)^2+(L/2)^2
R^2=R^2-2*H*R+H^2+L^2/4
2*H*R=H^2+L^2/4
R=H/2+L^2/(8*H)
3.\u4f8b\u98981\uff1a
\u5df2\u77e5\u5f26\u957f\u662f3295mm,\u62f1\u9ad8213mm,\u6c42\u534a\u5f84.
\u5f26\u957fL=3295mm,\u5f27\u9ad8H=213mm,\u6c42\u534a\u5f84R?R^2=(R-H)^2+(L/2)^2R^2=R^2-2*R*H+H^2+L^2/42*R*H=H^2+L^2/4R=H/2+L^2/(8*H)=213/2+3295^2/(8*213)=6477.99mm
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\u7b54\uff1a\u8bbe\u534a\u5f84\u4e3arr^2=(r-70)^2 + \uff08180/2\uff09^2
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R^2=(R-H)^2+(L/2)^2R^2=R^2-2*R*H+H^2+L^2/42*R*H=H^2+L^2/4R=H/2+L^2/(8*H)=0.4/2+0.85^2/(8*0.4)=0.426\u7c73
A=2*ARC SIN((L/2)/R)=2*ARC SIN((0.85/2)/0.426)=173.057\u5ea6=173.057*PI/180=3.02042\u5f27\u5ea6C=A*R=3.02042*0.426=1.286\u7c73

通过弧长得出圆心角A,设半径等于R,拱高H,COS角A=(R-H)/R就可以解出R了

设弦长2a,半径r,拱高h.

根据相交弦定理,a^2=h*(2r-h)

就可以求出r.

已知拱高h及弦长l,求弧长c?
弧半径为r,弧所对的圆心角为a。
r=h/2+l*l/(8*h)
a=2*arc
cos((r-h)/r)
c=π*r*a/180

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