Mathematics Question and Solution
Calculating Area Green Circle.
Let r be the radius of the circle.
16² = 18²+14²-2*18*14cosa
a = acos((18²+14²-16²)/(2*18*14))
a = 58.4118644948°
a is angle ADE.
b = 180-a
b = 180-58.4118644948
b = 121.588135505°
b is angle BDE.
(16/sin58.4118644948) = (18/sinc)
c = 73.398450401°
c is angle AED.
d = 180-c
d = 180-73.398450401
d = 106.601549599°
d is angle CED.
Calculating r, radius of the circle.
tan(0.5b) = r/e
e = r/tan(0.5*121.588135505)
e = 0.55901699438r units.
tan(0.5d) = r/f
f = r/tan(0.5*106.601549599)
f = 0.7453559925r units.
Notice.
e+f = DE = 14
It implies;
0.55901699438r+0.7453559925r = 14
(0.55901699438+0.7453559925)r = 14
r = 14/(0.55901699438+0.7453559925)
r = 10.733126292 units.
It implies, area green circle is;
πr²
= π(10.733126292)²
= 361.911473694 square units.
