Sir Mike Ambrose is the author of the question.
Notice!
AB = BC
Calculating AB.
AB = (20sin60)/sin104
AB = BC = 17.85075169007 cm.
Calculating BD
BD = (20sin16)/sin104
BD = 5.6815...
Let the side length of the inscribed green square be a.
b = ½(10-a) units.
c = b+a
c = ½(10-a+2a)
c = ½(10+a) units.
Therefore, a² (area green inscribed triangle) is;
10² = a²+(½(10+a...
Let OC be a.
Let the radius of the inscribed blue half circle be b.
Calculating area inscribed blue half circle.
20² = 2c²
c = √(200)
c = 10√(2) units.
d = ½(c)
d = 5√(2) units.
d i...
Let the side length of the two congruent inscribed squares be 1 unit each.
a² = 1+2²
a = √(5) units.
a is the radius of the half circle.
tanb = (½)
b = atan(½)°
(√(5)/sin(atan(½))) = (...
Let alpha be a.
Let AB be b.
tana = 2/b --- (1).
tana = b/(2+6)
tana = b/8 --- (2).
Equating (1) and (2).
2/b = b/8
b² = 16
b = 4 units.
Again, b is AB.
Therefore, the requir...
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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