Mathematics Question and Solution
Calculating the radius, R and circumference of the circle.
a² = 4²+8²-2*4*8cos60
a = 6.92820323028 units.
a is BD.
(6.92820323028/sin60) = (8/sinb)
b = 90°
b is angle BDC.
c² = 7²+4²-2*4*7cos120
c = 9.64365076099 units.
c is AD.
(9.64365076099/sin120) = (7/sind)
d = 38.9482755646°
d is angle ACD.
e = b+d
e = 90+38.9482755646
e = 128.9482755646°
e is angle ADB.
f = 360-2e
f = 360-2(128.9482755646)
f = 102.103448871°
f is angle AOB.
g = ½(f)
g = ½(102.103448871)
g = 51.0517244354°
h = ½(AB)
h = ½(7+8)
h = 7.5 units.
Calculating r, radius of the circle.
sin51.0517244354 = 7.5/r
r = 7.5/(sin51.0517244354)
r = 9.64365076099 units.
It implies;
Circumference of the circle is;
2πr
= 2*π*9.64365076099
= 60.592844769 units.
