Question

圆O1与圆O2相交于A.B两点，已知两圆的半径R1=10,R2=17,圆心距0102=21,则公共弦的

Answer 1

设公共弦长为x，两圆心连线与公共弦垂直相交点为P，从直角三角形各边长公式，可得：R1^2 - O1P^2 = R2^2 - O2P^2 ==> R1^2 - O1P^2 = R2^2 - (O1O2 - O1P)^2 ==>R1^2 - O1P^2 = R2^2 - O1O2^2 +2 x O1O2 x O1P - O1P^2 ==>O1P = (O1O2^2 + R1^2 - R2^2) / [2 O1O2] = (21^2 + 10^2 - 17^2) / (2 x 21) = 6O2P = O1O2 - O1P = 21 - 6 = 15故公共弦长度为： 2sqrt(R1^2 - O1P^2) = 2 sqrt (100 - 36) = 2 sqrt64 = 2 x 8 = 16