Calculating x (length BE).
sin60 = a/8
a = 4√(3) units.
a is DE.
cos60 = b/8
b = 4 units.
b is AD
c² = 2²+(2√(3))²
c = √(4+12)
c = 4 units.
d = (4+x) units.
Therefore, length x (BE) is;
Observi...
a² = 6²+8²-2*6*8cos30
a = 4.10628314132 cm.
a = DE.
(4.10628314132/sin30) = (8/sinb)
b = 103.06431342951°
b = Angle ADE.
Angle AED = 180-30-103.06431342951
= 46.93568657049°
tan30 = c/6
c = 3.46...
Notice, radius of the three congruent circles is 7 cm each.
sin60 = a/14
a = 7√(3) cm.
a = 12.124355653 cm.
b = a+7+7
b = (7√(3)+14) cm.
b = 26.124355653 cm.
b is the length of the rectangle.
tan...
a = ½(4+6)
a = 5 cm.
a is the radius of the ascribed semi circle.
Let b be the radius of the blue inscribed semi circle.
c = 5-4
c = 1 cm.
It implies;
b²+c² = d²
d² = b²+1²
d = √(...
a² = 12²-6²
a = 6√(3) cm.
a = 10.39230484541 cm.
a = circle's radius = AD = AG.
b² = 2*10.39230484541²-2*10.39230484541²cos120
b = 18 cm.
b = DG.
c = 12-10.39230484541
c = 1.60769515459 cm.
c = CD...
Calculating r, radius of the circle.
a*5 = 3*6
a = 18/5
a = 3.6 units.
a is Length BP.
b = ½(5+3.6)
b = 4.3 units
c = ½(3+6)
c = 4.5 units.
d = 4.5-3
d = 1.5 units.
It implies;
r² = b²+d²
r² =...
Let r be the radius of the inscribed circle.
a = (2-r) units.
(2-r)² = r²+b²
b² = 4-4r+r²-r²
b = √(4-4r) units.
c = (1+r) units.
d = (1+√(4-4r)) units.
It implies, observing Pythagoras Rule on...
Let a be the radius of the ascribed semi circle.
b = a-½(7)
b = (a-3.5) units.
15² = b²+c²
c² = 225+(a-3.5)²
c² = 225-(a²-7a+12.25)
c = √(225-a²+7a-12.25)
c = √(212.75+7a-a²) units.
Therefore;
a...
a = 1+2+1
a = 4 units.
a is the side length of the square.
tanb = 4/2
b = atan(2)°
tanc = 4/1
c = atan(4)°
d = 180-b-c
d = (180-atan(2)-atan(4))°
Observing Sine Rule.
(1/sin(180-atan(2)-atan(4))...
Notice!
Radius of the circle, r is;
r = √(50)
r = 5√(2) units.
a² = 2²+6²
a² = 4+36
a = √(40)
a = 2√(10) units.
tanb = 6/2
b = atan(3)°
c = ½(a)
c = ½(2√(10))
c = √(10) units....
