如图,在以O为圆心的两个同心圆中,小圆的半径长为2,大圆的弦AB与小圆交于点C、D,且AB=3CD,∠COD=60°.
2个回答

(1)过点O作OE⊥AB,

∵ OC=OD=2,∠COD=60°,AB=3CD

∴ CD=2,AB=6;

∵AE=1/2AB,∠A=∠COA=30°,

∴AE=3,AO=2√ 3;

(2)∵OF⊥AE,OF=2,AO=2√ 3,

∴AF=√(OA²-OF²)=2√ 2,

∴AE=2AF=4√ 2.