Let R = 1 unit.
sin22.5 = r/(1-r)
r = sin22.5-rsin22.5
r+rsin22.5 = sin22.5
r(1+sin22.5) = sin22.5
r = sin22.5/(1+sin22.5) units.
r = 0.2767686539 units.
It implies;
R/r
= 1/(sin22.5/(1+sin22.5))...
Let BC be 1 unit.
a = 180-60-20-40-10
a = 50°
a is angle ACB.
Observing Sine Rule.
(b/sin50) = (1/sin(60+20))
b = 0.7778619134 units.
b is AB.
c = 180-40-60
c = 80°
c is angle ADB....
Notice.
Radius of the ascribed circle is 7 cm.
Calculating a, radius of the big inscribed circle.
(7-a)² = 2a²
49-14a+a² = 2a²
a²+14a-49 = 0
Resolving the above quadratic equation via completing...
Calculating area green.
tana = 4/8
a = atan(½)°
b = 2a
b = 2atan(½)°
tanc = 8/4
c = atan(2)°
d = 2c
d = 2atan(2)°
It implies, area green is,
2(area sector with radius 4 units and angle 2atan(2...
Calculating yellow area.
It is;
2(area quarter circle with radius 4 units - area triangle with base and height 4 units respectively - area quarter circle with radius 3 units + area triangle with b...
Notice.
The ascribed plane shape is a regular pentagon with side length 10 units.
Let a be the radius of the bigger inscribed circle.
Radius of the smaller pink inscribed circle is r.
c = ⅕(180(5-...
Let BD = a
Notice!
BC = CD = BD = a
AC = 15 cm.
Half BD = ½(a) cm.
It implies;
sin60 = b/a
½√(3) = b/a
b = ½√(3)a cm.
Therefore;
½(a)+b = AC
½(a)+½√(3)a = 15
a+√(3)a = 30
a(1+√(3)) = 30
a = 10...
Let AC be 1 unit.
a = 180-12-15
a = 153°
a is angle ADC.
Observing Sine Rule.
(1/sin153) = (b/sin12)
b = 0.4579648493 units.
b is CD.
c = 180-12-18-15-33
c = 180-78
c = 102°
c is an...
Observing similar plane shape side lengths ratio.
3 - 5
a - (4-a)
Cross Multiply.
3(4-a) = 5a
12-3a = 5a
8a = 12
a = 3/2 units.
a is the base of the right-angled triangle with height 3 uni...
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