Let a be the side length of the two equal inscribed lengths.
r = 2+1
r = 3 units.
r is the radius of the ascribed half circle.
b²+(a/2)² = 3²
b²= 9-¼(a²)
b = √(9-¼(a²))
b = ½√(36-a²) unit...
a = (10+x) units.
a is the radius of the half circle.
(10+10)² = 16²+b²
b = √(400-256)
b = √(144)
b = 12 units.
It implies;
12 ~ c
20 ~ 10
Cross Multiply.
20c = 120
c = 6 units...
Let the radius of the circle be a.
sinb = a/(a+a)
b = 30°
cos30 = c/2a
c = √(3)a units.
d = 2-c
d = (2-√(3)a) units.
sin30 = e/d
e =½(2-√(3)a) units.
cos30 = f/d
½√(3) = f/(2-√(...
Sir Mike Ambrose is the author of the question.
Area S exact, or to 3 d.p. will be;
Area sector of radius 2√(7) units and angle (180 - 2sin–¹(4sin120÷(2√(7)))) + area triangle of two lengths 2...
Let the radius of the red circle be r.
Calculating r.
It will be;
√(13²-5²)=√((9+r)²-(9-r)²)+√((4+r)²-(4-r)²)
12=√(36r)+√(16r)
12=10√(r)
√(r)=1.2
r=1.44 units.
Calculating a...
Kindly move the question left/right one time to review the solution.
Thank you nicely.
Sir Mike Ambrose is the author of the question.
Let the radius of the inscribed semi circle be 1 unit.
Therefore;
Shaded area ÷ Rectangle area in it's simplest decimal form will be;
(0.25...
Sir Mike Ambrose is the author of the question.
Let the radius of one of the two equal circles be 1 unit.
Total shaded area ÷ Rectangle area will be;
(½(2x4)-π-(1-¼(4-π)-((180-2tan–¹(0.5))π÷...
Let x be the radius of the sector.
b = (x-1) units.
c = x+b
c = x+(x-1)
c = (2x-1) units.
Therefore;
5*3 = (2x-1)*1
15 = 2x-1
2x = 16
x = 8 units.
Again, a is the radius of the se...
x ~ 7
7 ~ y
Cross Multiply.
y = 49/x units.
Notice.
7 units is the radius of the green inscribed half circle.
x = 5 units.
x is the radius of the red inscribed half circle.
Therefor...
