Let a be the radius of the circle.
b² = a²+√(5)²
b = √(a²+5) units.
It implies;
2a ~ √(a²+5)
8 ~ a
Cross Multiply.
2a² = 8√(a²+5)
a² = 4√(a²+5)
a⁴ = 16a²+80
a⁴-16a²-80 = 0
Le...
r will be;
½(½(AB))
= ¼(AB)
Therefore;
r = ¼(1)
r = ¼ units.
Let the ascribed semi circle radius be R.
Let the inscribed circle radius be r.
Notice;
R=2r
It implies;
R²=1²+r²
(2r)²=1+r²
4r²=1+r²
4r²-r²=1
3r²=1
Therefore;
r =...
a ~ 6
6 ~ 8
Cross Multiply.
8a = 6*6
2a = 9
a = ½(9) units.
b = a+8
b = ½(9)+8
b = ½(25) units.
b is the diameter of the ascribed half circle.
c = ½(b)
c = ¼(25) units.
c is the...
Calculating area of the red inscribed circle.
Let a be the radius of the blue ascribed circle.
πa² =144π
a² = 144
a = 12 cm.
b = 2a
b = 24 cm.
b is the diameter of the blue ascribed cir...
Radius of the green circle is 4 units, therefore area of the green circle is;
π4²
= 16π square units.
Calculating radius of the red circle.
Let the radius of the red circle be r.
(4-...
Let 1 unit be the side length of the regular hexagon.
a = ⅙*180(6-2)
a = 120°
a is the single interior angle of the regular hexagon.
cos75 = 0.5/b
b = 1.93185165258 units.
c² = 1²+0.5²-...
Let the three equal inscribed lengths be y.
a = 5+4
a = 9 units.
a is the radius of the ascribed half circle.
b² = y²+y²
b = √(2)y units.
Notice.
a = b
√(2)y = 9
y = ½(9√(2)) uni...
Sir Mike Ambrose is the author of the question.
Let the radius of the semi circle be 3 units.
Therefore shaded area ÷ area square will be;
(½(area quarter circle of radius 3 units - area tri...
Let the radius of the ascribed quarter circle be R.
Let the radius of the inscribed circle be r.
Therefore;
2²+(2r)²=R²
4+4r²=R²
Therefore;
R²-4r²=4
Multiplying through by ¼(π)...
