a = ½(10)
a = 5 units.
a is the radius of the ascribed half circle.
cosb = 4/5
b = 36.8698976458°
b is angle alpha.
c²+8² = 10²
c = √(100-64)
c = 6 units.
sin(2acos(4/5)) = d/10
d = 9.6 units.
c...
Sir Mike Ambrose is the author of the question.
Let the single side length of the square be 2 units.
Calculating area S.
It will be;
Area trapezoid of two parallel side lengths 2 units an...
Using similar triangle approach.
It implies;
n ~ 1
n+1 ~ n
Cross multiply.
Therefore;
n²=n+1
n²-n-1=0
(n-½)²=1+¼
n =½±½(√(5))
Therefore;
n ≠ ½(1-√(5))
n = ½(1+√(5))...
Let length AB be x.
A careful analysis carried out on the given composite plane shape lead to the derivation of right-angled tiangle EQX with hypotenuse QX ⅓(4x) and the two adjacent side of the tr...
Calculating the radius of the two congruent inscribed circles.
Let the radius of the two congruent inscribed circles be a each.
b² = 3²+(2+2)²
b = √(25)
b = 5 units.
It implies;
(4*(3...
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...
