Question

已知大圆弧弦长540,弧高200,半径282,同心小圆弧与大圆弧上下距离均为34,求小圆弧弦长,弧高公式,

Answer 1

已知大圆弧弦长L1=540,弧高H1=200,半径R1=282,同心小圆弧与大圆弧上下距离均为34,求小圆弧弦长L2,弧高H2公式?

小圆弧半径为R2.

R1^2=(R1-H1)^2+(L1/2)^2

R1^2=R1^2-2*R1*H1+H1^2+L1^2/4

2*R1*H1=H1^2+L1^2/4

R1=H1/2+L1^2/(8*H1)

=200/2+540^2/(8*200)

=282.25

R2=R1-34=248.25

H2=H1-2*34=200-68=132

L2=2*(R2^2-(R2-H2)^2)^0.5

=2*(248.25^2-(248.25-132)^2)^0.5

=477.87