Question

如图,△ABC的三个顶点都在○O上,AB为直径,CD平分∠ACB,∠CAB=30°,求AB AD和BD 的长

Answer 1

是不是这个

三角形abc的三个顶点都在圆o上,ab为直径 ==> ∠C = 90°；==>RtΔCAB

∠CAB = 30° ==> BC = 1/2 *AB；

AC = √3/2 *AB

∴ AB = AC/(√3/2) = 2√3 ；BC =1/2 *AB = √3

CD平分角ACB ==> AD：BD = AC：BC = 3：√3 --- (1)

而：AD+BD = AB = 2√3 --- (2)

(1)(2)联立,解得：

AD = 3√3-3；BD=3-√3