Mathematics Question and Solution
a =1
b = 0.5
Cross Multiply.
b = 0.5a ----- (1).
½(a)+½(a)+½(1*0.5)+½(1-b) = 1
2a+0.5+1-b = 2
2a-b = 0.5
b = 2a-0.5 ---- (2).
Equating (1) and (2).
2a-0.5 = 0.5a
1.5a = 0.5
a = (1/2)/(3/2)
a = ⅓ units.
b = 0.5a
b = 0.5*(⅓)
b = ⅙ units.
c² = (⅓)²+(⅙)²
c = 0.37267799625 units.
d² = 0.37267799625²+1²-0.37267799625*2cos(atan2)
d = 0.89752746786 units.
e = √(0.5²+1²)-0.37267799625
e = 0.7453559925 units.
f = 0.7453559925²+0.5²-2*0.5*0.7453559925cos(180-atan2)
f = 1.06718737291 units.
g = 1-b
g = 1-(⅙)
g = (5/6) units.
Where g is the height of the triangle ascribing the circle.
Calculating r, radius of the inscribed circle.
½(0.89752746786r)+½(1.06718737291r)+½(r) = ½(5/6)*1
0.89752746786r+1.06718737291r+r = (5/6)
2.96471484077r = (5/6)
r = (5/6)/2.96471484077
r = 0.28108380674 units.
