Calculating blue area (area triangle BDE).
a = ½(32+7)
a = ½(39)
a = 19.5 units.
a is the radius of the ascribed half circle.
b = 19.5-7
b = 12.5 units.
12.5² = 17²+19.5²-2*17*19.5cosc...
Sir Mike Ambrose is the author of the question.
Calculating Area Lilac ÷ Area Large Square.
Let the radius of the semi circle be 1 unit.
Therefore;
Area lilac is;
Area triangle with he...
Sir Mike Ambrose is the author of the question.
Calculating Area Blue ÷ Area Green in its simplest form.
Let the single side length of the regular octagon be 2 units.
Therefore;
Area gre...
Calculating r, radius of the circle.
a = (r-4) units.
b = a+r
b = (2r-4) units.
8c = 4(2r-4)
c = (r-2) units.
d = 8+c
d = (6+r) units.
e² = 2r²+2r²cos120
e² = 3r²
e = √(3)r unit...
Calculating r, radius of the half circle.
Let x be the diameter of the half circle.
x² = 16²+a²
a = √(x²-256) units.
b = a-21
b = (√(x²-256)-21) units.
c = (x-7) units.
Calculating...
Calculating r, radius of the half circle.
a²+9² = 23²
a = 8√(7) units.
a = 21.1660104885 units.
tanb = 8√(7)/8
b = atan(8√(7)/9)°
c = (r-5) units.
(r-5)² = d²+(½*8√(7))²
r²-10r+25...
Calculating r, radius of the half circle.
a²+14² = (2r)²
a = √(4r²-196) units.
b = (r-2) units.
√(4r²-196)² = 2²+7²-28cosx
4r²-196 = 53+28cosx
28cosx = 4r²-249
cosx = (4r²-249)/2...
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Calculating green area.
a = (6+x) units.
a is the radius of the circle.
b = a-2
b = (6+x)-2
b = (4+x) units.
(6+x)² = (4+x)²+c²
36+12x+x² = 16+8x+x²+c²
c² = 20+4x
c = √(20+4x) units....
Let the required angle be x.
5 units, 3 units and 2 units are the radii respectively of each of the circles, decreasingly.
Calculating x.
a = 5+2
a = 7 units.
b = 5-2
b = 3 units....
