Question

如图.在圆O中,AB是直径,CD是弦.且CD平分∠ACB.∠ADC=30°,AC=4

Answer 1

(1)△ADB是怎么样的△,说明理由,

△ADB是个直角三角形,因为AB是直径,点D在圆上.

(2）分别求出CB,AD,CD的长

角ACB=90度

角ACD=角BCD=角ACB/2=45度

角ADC=30度

角CAD=180-角ACD-角ADC=180-45-30=105度

AD/SIN(角ACD)=AC/SIN(角ADC)

AD=(AC/SIN(角ADC))*SIN(角ACD)=(4/SIN(30))*SIN(45)=5.6569

CD=(AC^2+AD^2-2*AC*AD*COS(角CAD))^0.5

=(4^2+5.6569^2-2*4*5.6569*COS(105))^0.5

=7.33869

角CDB=90-角ADC=90-30=60度

角CBD=180-角CDB-角BCD=180-60-45=75度

CD/SIN(角CBD)=BD/SIN(角BCD)=BC/SIN(角BDC)

BD=(CD/SIN(角CBD))*SIN(角BCD)

=(7.33869/SIN(75))*SIN(角45)

=5.3723

BC=(CD/SIN(角CBD))*SIN(角BDC)

=(7.33869/SIN(75))*SIN(60)

=6.5797