Mathematics Question and Solution
Notice!
Length 3 units and length 6 units are both tangent to the green inscribed circle.
It implies;
Radius r, of the ascribed semi circle is;
r = ½(3+6)
r = ½(9)
r = 4.5 units.
Where 9 units is the diameter of the ascribed semi circle.
9² = 5²+6²-2*5*6cosa
81 = 61-60cosa
60cosa = 61-81
cosa = (-20/60)
a = acos(-1/3)
a = 109.4712206345°
a is angle ADB.
b = 180-a
b = 180-109.4712206345
b = 70.5287793655°
b is angle BDC.
Let length CD, the required length be x.
It implies;
cos70.5287793655 = x/6
x = 6cos70.5287793655
x = 2 units.
CD = 2 units.
