Sir Mike Ambrose is the author of the question.
Let the ascribed circle's radius be 1 unit.
Area ascribed circle is;
π(1)²
= π square units.
Calculating shaded area.
Notice.
The side...
Sir Mike Ambrose is the author of the question.
Let AB be 2 units.
Area ABCD is;
2²
= 4 square units.
Let the side length of the ascribed square be x.
Calculating x.
a = (x-2) unit...
Let the two equal smaller inscribed circle radius be r.
Let the radius of the smallest inscribed circle be q.
The radius is the biggest inscribed circle is 0.5 units.
Therefore;
x+2r=0....
Length EF will be;
√(49+50-70√(2)cos(tan-¹(¾)+45))
EF = √(85) units.
Notice.
r, radius of the ascribed half circle is 5 units.
Calculating the area of the inscribed red circle.
Let it's radius be x.
Calculating x.
a = (5-x) units.
tan15 = x/b
b =...
Area Black will be;
Area triangle BCD - area sector of radius 4m and angle 45° + area sector of radius 4m and angle 45° - quarter circle of radius 2m - 2(right-angled triangle of height and base...
Let MN=NP=PD=MD=y.
Let AR=x.
Therefore;
AD=AB=BC=CD=2+x.
RD=2.
RM=2-y.
And;
RC=2+2x.
There deriving an equation.
Considering similar triangle RCD and RNM.
It implies;
2-y=2
...
Radius R of the big circle is 50 unit.
(R-10)²=R(R-18)
R²-20R+100=R²-18R
2R=100
R=50 units.
Radius r of the small inscribed unshaded circle is 41 unit.
2r=2R-18, and R=50
2r=100-18
2r=82...
Let the radius of the ascribed quarter circle be 2x.
Therefore the radius of the inscribed yellow half circle is x.
Calculating x.
¼(π(2x)²)-½(πx²) = 17
πx²-½(πx²) = 17
2πx²-πx² = 34...
