Let the diameter of the inscribed circle be 1 unit.
Therefore, the radius of the ascribed semi circle is 1 unit.
Calculating angle a°.
b = 0.5 unit.
c = 1.5 units.
Therefore, angle a° is;
atan(...
Let the length and width of the ascribed rectangle be 3 units and 2 units respectively.
Calculating red area.
It is;
Area quarter circle with radius 2 units - Area sector with radius 1.5 units and...
a² = 9
a = √(9)
a = 3 cm.
a is the side of square ABCD.
b² = 3²+3²
b = √(18)
b = 3√(2) cm.
b is AC = BD.
c = ½(b)
c = ½(3√(2))
c = 1.5√(2) cm.
c = AQ = BQ.
Let DE = d.
e = (3+...
Calculating h, height of the ascribed right-angled triangle.
Notice, 4 units is the radius of the inscribed circle.
a² = h²+40²
a= √(h²+1600) units.
a is the hypotenuse of the ascribed right-angle...
Calculating r, radius of the circle.
8² = 9²+7²-2*9*7cosa
cosa = (9²+7²-8²)/(2*7*9)
a = acos((9²+7²-8²)/(2*7*9))
a = 58.4118644948°
(8/sin58.4118644948) = (9/sinb)
b = 73.398450401°
c = ½(180-a)...
Let the side length of the green square be x.
Notice, radius of the two congruent circles is 5 units each.
Therefore;
a = (5-x) units.
b = (5-½(x)) units.
Observing Pythagoras Rule t...
Let BC be 1 unit.
a = 180-57-49-33
a = 180-139
a = 41°
a is angle BDC.
Observing Sine Rule.
(1/sin41) = (b/sin(49+33))
b = 1.5094191604 units.
b is BD.
c = 180-33-30-41
c = 180-104
c = 76°
c is a...
Sir Mike Ambrose is the author of the question.
Area Green exactly is;
Area trapezoid with parallel sides 3 cm and (6-2√(3)) cm, and height (6-3√(3)) cm.
= ½(6-3√(3))(3+(6-2√(3)))
= ½(6-3√(3))(9-...
Let AB = 1 unit.
Calculating CD.
a = 180-40-60
a = 80°
a is angle ADB.
Observing Sine Rule.
(1/sin80) = (b/sin40)
b = 0.6527036447 units.
b is AD.
c = 180-80
c = 100°
c is angle ADC.
d = 180-1...
Calculating R, radius of the circle.
5² = (½(8))²+a²
25 = 16+a²
a = √(25-16)
a = 3 units.
b = (R-3) units.
Therefore, R is;
R² = (R-3)²+(½(8))²
R² = (R-3)²+4²
R² = R²-6R+9+16
6R = 25...
