Question

求扇形面积：已知AB是半圆o的直径,C在半圆O上,CD垂直AB于D,E在CD上,圆E与AB相切于点D,与半圆O相切于

Answer 1

1,OC=AB/2=6/2=3

2,设圆E半径为r

OD=√(OC^2-CD^2)=√3

OE=OF-r=3-r,ED=r

ED^2+OD^2=OE^2

r^2+3=(3-r)^2

r=1

3,阴影面积=扇形(BOF)-扇形(DEF)-三角形(ODE)

tan(EOD)=ED/OD=√3/3,∠FOB=30

∠OED=90-30=60

∠DEF=180-60=120

S扇形(BOF)=π*3^2*30/360=3π/4

S扇形(DEF)=π1^2*120/360=π/3

S三角形(OED)=OD*OE/2=√3/2

S阴影=3π/4-π/3-√3/2

=π/3-√3/2