Mathematics Question and Solution
Calculating R, radius and circumference of the ascribed circle.
a = √(3) units.
a is the side length of the blue inscribed square.
b = √(5) units.
b is the side length of the green inscribed square.
c = √(7) units.
c is the side length of the red inscribed square.
√(5)² = √(3)²+√(7)²-2√(3)*√(7)cosd
2√(21)cosd = 10-5
cosd = 5/(2√(21))
d = 56.9381038653°
d is the angle opposite √(5) units.
(√(5)/sin56.9381038653) = (√(7)/sine)
e = 82.5824442091°
e is the angle opposite √(7) units.
f = 180-d
f = 180-56.9381038653
f = 123.061896135°
g² = √(3)²+√(7)²-2√(3)*√(7)cos123.061896135
g = 3.87298334621 units.
(3.87298334621/sin123.061896135) = (√(7)/sinh)
h = 34.9260568561°
j² = 2√(3)²
j = √(6) units.
k = 180-e+½(90)
180-82.5824442091+45
k = 142.417555791°
l² = √(5)²+√(6)²-2√(5)*√(6)cos142.417555791
l = 4.43634373644 units.
(4.43634373644/sin142.417555791) = (√(5)/sinm)
m = 17.903305623°
n = h+45+m
n = 34.9260568561+45+17.903305623
n = 97.8293624791°
o² = g²+l²-2*g*lcos97.8293624791
o² = 3.87298334621²+4.43634373644²-2*3.87298334621*4.43634373644cos97.8293624791
o = 6.27393747942 units.
o is a chord of the ascribed circle.
p = 360-2n
p = 360-2(97.8293624791)
p = 164.341275042°
q = ½(p)
q = ½(164.341275042)
q = 82.170637521°
Calculating R, radius of the ascribed circle.
sin82.170637521 = ½(o)/R
R = (0.5*6.27393747942)/sin82.170637521
R = 3.16648621774 units.
Calculating C, circumference of the ascribed circle.
C = 2πR
C = 2*π*3.16648621774
C = 19.8956196787 units.
