如图,已知AB是圆o的直径,弦CD交AB于E点,BE=1,AE=5,角AEC=30度,求CD的长图中弦DC交直径弦BA于点E

Question

如图,已知AB是圆o的直径,弦CD交AB于E点,BE=1,AE=5,角AEC=30度,求CD的长
图中弦DC交直径弦BA于点E

Answer 1

过O作OF⊥CD
∵AE＝1,BE＝5
∴AB＝AE+BE＝1+5＝6
∴AO＝AB/2＝6/2＝3
∴OE＝AO-AE＝3-1＝2
∵∠AEC＝45
∴∠OEF＝45
∵OF⊥CD
∴OF＝OE×√2/2＝√2
∴CF＝√（OC²-OF²）＝√（9-2）＝√7
∴CD＝2CF＝2√7