Calculating x, length DF.
Let a be the radius of the ascribed half circle.
b = (a-6) units.
c = (a-7) units.
7² = 6²+8²-2*6*8cosd
96cosd = 36+64-49
d = acos((36+64-49)/96)
d = 57.910...
Calculating the chord length.
Let x be the radius of the half circle.
a = (x-4) units.
b = (x-9) units.
c = (x-7) units.
d = a+b
d = (x-4)+(x-9)
d = (2x-13) units.
d is the length...
Area Orangle ÷ Area Large Square to 3 d. p.
Let the side length of the large square be x.
Calculating x.
25=x²+64-(16xcos20)
Therefore;
x = 11.70244 cm
It implies;
Area large square is;
11.7...
Calculating R, radius of the circle.
(4√(2))² = 1+5²-2*5cosa
32 = 26-10cosa
16 = 13-5cosa
cosa = (-3/5)
a = 126.869897646°
b = 360-2a
b = 360-2*126.869897646
b = 106.260204708°
c = ½...
Calculating r, radius of the circle.
Let theta be x.
Notice.
BC = CD, let it be a.
a² = 2²+13²-2*2*13cosx
a² = 173-52cosx --- (1).
a² = 11²+13²-2*11*13cosx
a² = 290-286cosx --- (2)...
Calculating area of the ascribed circle.
Let r be the radius of the ascribed circle.
a = 3+2
a = 5 units.
a is the side length of the inscribed regular triangle (equilateral triangle).
s...
Calculating Area Orange.
tana = 3/6
a = atan(½)°
sin(atan(½)) = b/3
b = 1.3416407865 units.
cos(atan(½)) = c/3
c = 2.683281573 units.
d = √(6²+3²)
d = √(45)
d = 3√(5) units.
e²...
Notice.
The composite plan shape is not drawn to scale.
Calculating the inscribed orange triangle area.
Notice Again.
3 units is the diameter of the inscribed circle.
a = ½(3)
a = 1.5 uni...
Calculating R, radius of the inscribed circle.
cosa = BA/BC
a = acos(4/8)
a = 60°
a is angle ABC.
b = ½(a)
b = 30°
b is angle ABD = angle CBD.
sin30 = c/8
c = 4 cm.
c is CD.
cos3...
Calculating length BP.
Let CQ = a.
b = (16+a) units.
b is CD = AC, the radius of the ascribed half circle.
c = b-5
c = (11+a) units.
c is BC.
e² = a²+(11+a)²-2a(11+a)cos120
e² = 2a²...
