Calculating x, the side length of the ascribed square.
a²+x² = 8²
a = √(64-x²) units.
b²+x² = 10²
b = √(100-x²) units.
It implies;.
c = (x-√(64-x²)) units.
d = (x-√(100-x²)) units.
Therefore;...
Let the radius of the quarter circle be 1 unit.
b = (a+1) units.
a is AD = DE.
a² = 2-2cosx
2cosx = 2-a²
cosx = ½(2-a²) --- (1).
cosx = 1/(1+a) --- (2).
Calculating a.
Equating (1...
Calculating Area Inscribed Red Circle.
a = ½(8)
a = 4 units.
a is the radius of the two congruent half circles.
b = (4+x) units.
x is the radius of the red inscribed circle.
c = (4-x) units.
The...
Calculating r, radius of the circle.
Notice that the plane shape is not drawn to scale.
r² = (7+a)²+(0.5*10)²
r² = 49+14a+a²+25
r² = 74+14a+a² --- (1).
Again.
r² = a²+(7+5)²
r² = a²+...
Calculating r, radius of the half circle.
Let the two equal lengths be a each.
Therefore;
r = 2a units.
Calculating a.
(2a)² = a²+9²-2a*9cosb
3a² = 81+18acosb
cosb = (3a²-81)/(18a)
cosb = (a...
Calculating shaded area.
tana = 5/10
a = atan(½)°
Therefore;
b = atan(2)°
c = 90-2a
c = 90-2atan(½)
c = 36.8698976458°
d = 180-2b
d = 180-2atan(2)
d = 53.1301023542°
Shaded A...
Calculating x.
a = 2*120
a = 240°
b = 360-a
b = 120°
c = ½(180-120)
c = 30°
d = 2*140
d = 280°
e = 360-d
e = 80°
f = ½(180-80)
f = 50°
It implies;
x = c+f
x = 30+50
x = 80°
Notice.
r is the radius of the inscribed yellow half circle.
r = ½(10)
r = 5 units.
Calculating R, radius of the ascribed circle.
Calculating R.
a = x+10+5
a = (x+15) units.
b = ½(a)
b = ½(x+1...
Kindly move the question right or left one time to review the solution and answer.
Solution and answer by Mehmet Kara.
Thank you nicely.
Let AC = BD = DE = a.
Calculating a.
14² = a²+(10+a)²-2a(10+a)cosb
96 = 2a²+20a-(20a+2a²)cosb --- (1).
14² = a²+10²+2a*10cosb
96 = a²+20acosb
cosb = (96-a²)/(20a) --- (2).
Substituting (2) in (1...
