Mathematics Question and Solution
Calculating Angle x.
Let 1 unit be the radius of the quarter circle.
Let y be the radius of the inscribed circle.
Notice.
OB = BD.
OC = 8 cm, radius of the quarter circle.
a = ½(OC)
a = ½(8)
a = 4 units.
a is half the radius of the ascribed quarter circle.
sinb = 4/8
b = asin(½)
b = 30°
b is angle BOD = angle BDO
c = ½(180-b)
c = ½(180-30)
c = ½(150)
c = 75°
c is angle CDO = angle DCO.
Therefore, the required angle, x is
x = c-b
x = 75-30
x = 45°
Again, x is the required angle.
Calculating r, radius of the inscribed circle.
d = (8-r) cm.
It implies;
sinb = r/(8-r)
And b = 30°
sin30 = r/(8-r)
½ = r/(8-r)
2r = 8-r
3r = 8
r = ⅓(8) cm.
