Question

已知圆中,弦AB=2倍的根号3分之1,弦心距为1,则圆的半径是多少?

Answer 1

已知圆中,弦AB=L=2*(1/3^0.5),弦心距为H=1,则圆的半径R是多少?

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)

=1/2+(2*(1/3^0.5))^2/(8*1)

=1/2+(4*(1/3))/8

=1/2+(4/3)/8

=1/2+1/6

=4/6

=2/3