Mathematics Question and Solution
The radius of the circle is 6 cm.
a = atan(2)°
Where a is angle AOB = angle COE.
Angle BOE = 180-atan(2)
= 116.56505117708°
Angle OBE = ½(180-116.56505117708)
= 31.71747441146°
b = 90+31.71747441146
b = 121.71747441146°
Where b is angle ABE.
(12/sin31.71747441146) = (c/sin121.71747441146)
c = 19.416407865 cm.
Where c is AE.
sin(atan2) = d/19.416407865
d = 17.366563146 cm.
cos(atan2) = e/19.416407865
e = 8.683281573 cm.
f = 12-8.683281573
f = 3.316718427 cm.
g = atan(3.316718427/17.366563146)
g = 10.81231696357°
h = 10.81231696357+atan(1/2)
h = 37.37736814065°
i = 180-37.37736814065-atan(2)
i = 79.18768303643°
j = ½(180-atan(2))
j = 58.28252558854°
k = 58.28252558854-37.37736814065
k = 20.90515744789°
l = 180-20.90515744789-atan2
l = 95.65989372919°
(6/sin95.65989372919) = (m/sin20.90515744789)
m = 2.15142104182 cm.
Therefore;
Area Shaded is;
0.5*2.15142104182*6sin(atan2)
= 5.77286843728 cm²
