已知圆上两点间距离25m,中间点到圆边距离3m,求两点间圆弧长度,和圆的半径

Question

已知圆上两点间距离25m,中间点到圆边距离3m,求两点间圆弧长度,和圆的半径

Answer 1

已知圆上两点间距离L=25m,中间点到圆边距离H=3m,求两点间圆弧长度C,和圆的半径R?
弧所对的圆心角为A.
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)
=3/2+25^2/(8*3)
=27.5417m
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((25/2)/27.5417)
=53.983度
C=π*R*A/180=π*27.5417*53.983/180=25.9492m