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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Thank you amazingly.
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....
Sir Mike Ambrose is the author of the question.
Calculating Area Purple ÷ Area Rectangle.
Let the single side length of the three side regular hexagon be 1 unit.
Therefore;
The width of t...
Calculating Length x (AC).
Notice.
BC = AD = 9 units.
a = 9+7
a = 16 units.
a is BD.
It implies;
9² = 15²+16²-2*15*16cosb
81 = 225+256-480cosb
480cosb = 481-81
cosb = 400/480
b...
Calculating Blue Area.
a = (14-x) cm.
Calculating x.
10² = x²+(14-x)²
100 = x²+196-28x+x²
2x²-28x+96 = 0
x²-14x+48 = 0
x²-6x-8x+48 = 0
x(x-6)-8(x-6) = 0
(x-6)(x-8) = 0
It implies;...
