Question

两个同心圆的半径分别为2和4,大圆的弦AD交小圆于B,C两点,且AB=BC=CD.则AB的长等于

Answer 1

设 弦高OE=x,AE^2=4^2-x^2=16-x^2 ；BE^2=2^2-x^2=4-x^2

根据题意,AE=AB+BE=AE+BC/2=3AB/2=3BE,所以 AE^2=9BE^2,即 16-x^2 =9(4-x^2)

x^2=5/2

BE^2 =4-5/2=3/2

BE=2分之 √6

AB=3BC=6BE=3√6