Calculating angle alpha.Let the side length of the ascribed square be 1 unit.Therefore, the side length of the inscribed green regular triangle 1 unit.a = 90-60°a = 30°b² = 2-2cos30b = 0.51763809021...
Calculating the required inscribed area, area pink shaded triangle.Let a be the side length of the two equal inscribed lengths.r = 2+1r = 3 units.r is the radius of the ascribed half circle.b²+(a/2)²...
Calculating the red length.Notice the green length is the diameter of the small circle.Length green = 2*2 = 4 units.Let a be the radius of the big circle.b = (4-a) units.c = 2+bc = 2+(4-a)c = (6-a) u...
Calculating r, radius of the inscribed circle.Let the ascribed circle's radius be a.a = ½(b+b+8)a = (b+4) units.c = a-b-bc = (b+4)-b-bc = (4-b) units.Calculating b.a² = c²+4²(b+4)² = (4-b)²+4²b²+8b+1...
Calculating x.tana = 3/1.5a = atan(2)°b = 3+1.5b = 4.5 units.c = 3+1+xc = (4+x) units.Calculating x.It implies;tan(atan(2)) = c/b2 = (4+x)/4.52 = (4+x)/(9/2)2 = 2(4+x)/918 = 8+2x10 = 2xx = 5 units.
Let FO be r, radius of the ascribed circle.a²+r² = (2+3)²a = √(25-r²) units.b = a+rb = (r+√(25-r²)) units.c = r-ac = (r-√(25-r²)) units.Therefore;4*(2+3) = (r-√(25-r²))(r+√(25-r²))20 = r²-(25-r²)20 =...
Calculating the red length.a² = 3²+4²a = √(25)a = 5 units.a is the hypotenuse of the ascribed right-angled triangle.tanb = 3/4b = atan(3/4)°tanc = 4/3c = atan(4/3)°Let d be the radius of the inscribe...
Calculating Length x (AD).Let a be the diameter of the green inscribed circle.Therefore;x ~ a(b+x) ~ 2aCross Multiply.2ax = ab+ax2ax-ax = abax = abx = b units.Therefore, length x is;x*x = 9*4x² = 36x...
Calculating Inscribed Square Area.Notice.The ascribed right-angled triangle is not drawn to scale.Let a be the side length of the inscribed square.Calculating Area Inscribed Square.tanb = 3√(3)/(9√(3...
Calculating x.Notice.The angle formed at the meet point (vertex) of length 4 units and x units is equal the angle formed at the meet point (vertex) 9 units and x units.It implies, two similar plane s...
