Mathematics Question and Solution
a = ½(21-11)
a = ½(10)
a = 5 units.
sinb = 5/13
b = asin(5/13)
b = 22.619864948°
c = b+90
c = 112.619864948°
c is angle ABC = angle BCD.
d = ½(360-2c)
d = ½(134.7602701039)
d = 67.380135052°
d is angle BAD = angle ADC.
e² = 13²+11²-2*11+13cos112.619864948
e = 20 units.
Or
e² = 21²+13²-2*21*13cos67.380135052
e = 20 units.
Radius blue inscribed circle, r is;
13r+11r+20r = 11*13sin112.619864948
44r = 132
r = 3 units.
Radius yellow inscribed circle, R is;
21R+13rR+20R = 21*13sin67.380135052
54R = 252
R = ⅓(14) units.
It implies;
R+r is;
⅓(14)+3
= ½(14+9)
= ⅓(23) units.
