一未知圆形从边到圆心取半径的H=700为点画一条垂直与此半径的直线交于圆边的两点A和B,线段AB长L=1800,求圆的半径R是多少?弧长C多少?
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)
=700/2+1800^2/(8*700)
=350+4050/7
=6500/7
=928又(4/7)
=928.571
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((1800/2)/928.571)
=151.5度
=151.5*PI/180
=2.644弧度
C=A*R
=2.644*928.571
=2455.3