Mathematics Question and Solution
Calculating R.
b = 60°
b is the single interior angle of the ascribed regular triangle (equilateral triangle).
c = ½(b)
c = 30°
tan30 = R/d
1/√(3) = R/d
d = √(3)R cm.
e = R+R
e = 2R cm.
f = 2d+e
f = 2√(3)R+2R
f = 2R(1+√(3)) cm.
Notice.
f = a
Therefore, R is;
2R(1+√(3)) = 6
R = 3/(1+√(3))
R = 3(1-√(3))/(1-3)
R = ½(3(√(3)-1)) cm.
R = 1.09807621135 cm.
R is the radius of each of the three congruent inscribed circles.
