Let a be the radius of the circle.
b = 2a units.
b is the diameter of the circle.
Observing similar plane shape (right-angled) side length ratios.
6 - 2a
a - 10
Cross Multiply.
2a²...
Let BC be a.
Let alpha be b.
tanb = 24/a --- (1).
tan(2b) = (24+26)/a
tan(2b) = 50/a
2tanb/(1-tan²b) = 50/a --- (2).
Substituting (1) in (2).
2(24/a)/(1-(24/a)²) = 50/a
(48/a)/(...
Sir Mike Ambrose is the author of the question.
Let the single side length of the square be 2 unit.
Calculating area S.
It is;
Area trapezoid of two parallel side lengths 2 unit and (2-√(3)...
a = 180-30-33
a = 117°
b+117+15+33+30+39 = 360
b = 360-180-54
b = 126°
c+126+30+9+39+57 = 360
c = 99°
d = 180-99-9
d = 180-108
d = 72°
e = a-57
e = 117-57
e = 60°
f = 180-60-...
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Considering similar triangle (scalene) side length ratios.
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(...
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...
Calculating x (length OD).
a = (x+4) units.
a is the radius of the quarter circle (length OA = length OB).
It implies;
(x+4)² = 8²+x²
x²+8x+16 = 64+x²
8x = 48
x = 6 units.
Again, x is...
Area Coloured Region is;
Area triangle with height and base 10 units - Area triangle with height and base 3√(2) units - Area triangle with height 5 units and base 7√(2)sin45 units
= ½*10*10)...
Calculating the area of the inscribed blue circle.
a = ½(14+6)
a = 10 units.
a is the radius of the ascribed semi circle.
b = a-6
b = 4 units.
c²+4² = d²
c is the radius of the inscrib...
