radian measure....

圖片參考：http://i295.photobucket.com/albums/mm158/Audrey_hepburn2008/A_Hepburn01Aug231441.jpg?t=1219473748


a. Draw O2E, O2E is perpendicular to O1D.

O1E = ED - O2C = 17 - 8 = 9 cm

CD = O2E = √[412 - 92] = 40 cm

∠O1O2E = cos-1(40/41)

∠O2O1E = cos-1(9/41)

∠BO2C = 2π - π/2 - π/2 - 2cos-1(40/41) = π - 2cos-1(40/41)

Length of arc BC = O2B X ∠BO2C = 21.5917 cm

Major ∠AO1D = 2π - 2cos-1(9/41)

Length of major arc AD = O1D X Major ∠AO1D

= 60.9318 cm

So, length of the belt

= 60.9318 + 21.5917 + 40 + 40

= 162.52 cm (cor. to 2 d.p.)


b. Area of tranpezium O1O2CD = Area of O1O2BA

= (8 + 17)(40) / 2 = 500 cm2

Area of sector BO2C

= 1/2 (8)2(π - 2cos-1(40/41))

= 86.3668 cm2

Area of major sector AO1D

= 1/2 (17)2(2π - 2cos-1(9/41))

= 517.92 cm2

Area enclosed by the belt

= 517.92 + 500 X 2 + 86.3668

= 1604.28 cm2 (cor. to 2 d.p.)