Question

扇形OAB的弦AB=18,半径为6的圆C恰与OA、OB和弧AB相切,圆D又与圆C、OA和OB相切,则圆D的半径为____

Answer 1

圆C半径R=6

做CE⊥OB于E,DF⊥OB与F

CE=R=6,DF=r

OC=OB-R=OB-6

OD=OB-2R-r=OB-12-r

DF/OD=CE/OC=1/2AB/OB

r/(OB-12-r) = 6/(OB-6) = 1/2*18/OB

由6/(OB-6) = 1/2*18/OB=9/OB

9OB-9*6=6OB

OB=(9*6)/(9-6)=18

带入r/(OB-12-r) = 6/(OB-6)

r/(18-12-r) = 6/(18-6)

r/(6-r) = 1/2

6-r = 2r

3r=6

r=2

圆D的半径为2