Mathematics Question and Solution
Calculating angle BAC, an interior angle of the inscribed triangle ABC.
0.5*15*18sinx = Area triangle ABC
135sina = 81
sinx = (81/135)
x = asin(81/135)
x = 36.8698976458°
x again, is angle BAC.
a² = 15²+18²-2*15*18cos36.8698976458
a = 10.8166538264 units.
a is BC.
b = ½(a)
b = ½(10.8166538264)
b = 5.4083269132 units.
Let O be the centre of the circle.
c = 2x
c = 2*36.8698976458
c = 73.7397952916°
c is angle BOC.
d = ½(c) = x = 36.8698976458°
It implies, r, radius of the circle is;
sin36.8698976458 = b/r
sin36.8698976458 = (5.4083269132/r)
r = (5.4083269132/sin36.8698976458)
r = 9.0138781887 units.
