Radius, r of the semi circle is;
Cos(2atan(1/(4+√(7))))=(5+√(7))/d
Notice;
d = 2r
Therefore,
d = (5+√(7))/Cos(2atan(1/(4+√(7))))
d = 8 units.
And d = 2r
2r = 8
r (radius semi...
Sir Mike Ambrose is the author of the question.
(a) Exact radius of the circle is;
r = ½√(2²+4²)
r = ½√(20)
r = ½*2√(5) units.
r = √(5) units.
Or
Cos(atan(2)) = (1/r)
Where r is the...
r, radius of the ascribed circle will be;
½(r²)sin60=(256/6)
½√(3)r²=⅓(256)
3√(3)r²=512
r²=(512√(3))/9
r = ⅓√(512√(3)) units.
r = 9.92645183043 units
r ≈ 10 units.
Let a be 2 unit.
b will be;
(2+b)²=2(2-b)²
4+4b+b²=8-8b+2b²
b²-12b+4=0
(b-6)²=-4+36
b = 6±√(32)
It implies;
b ≠ 6+√(32)
b = 6-√(32)
b = 6-4√(2)
b = 2(3-2√(2)) units.
Therefore;...
Let x be the radius of the inscribed green circle.
Therefore radius of the ascribed semi circle, r will be;
r = 2x
Therefore;
2*2=3x*x
4=3x²
x (green circle radius) is;
x = √(4...
Calculating r, radius of the inscribed semi circle.
49r²-168r+144 = 0
Therefore;
r = 12/7 units.
It implies;
Calculating x.
x = 5-2(12/7)-(23/20)
x = 59/140 units.
Shaded Area is;
(13*8)-½(11*8)-2(½(13*4))+½(2+13)*8
= 104-44-52+60
= 164-96
= 68 square units.
Let YC, radius of the small circle be r.
Notice;
XY = CD = AD = AB = BC = single side length of square ABCD.
Calculating r.
πr² - ½(πr²) - 90π(XY)²/360 + ½(XY)² = 1
XY will be;
√(r²+r²...
Let the length and width of the rectangle be y and z respectively.
Therefore;
7+7+x+y+z+7+7+x+y+z=66
Where 7 is the single side length of the square.
It implies;
14+14+2x+2y+2z=66
Th...
Let the radius of the semi circle be r.
Calculating r.
2+√(5/2)r - ½(3r)
2r - √(5/2)r
Cross multiply.
3r² = 2√(5/2)r + (5/2)r²
(½)r² = 2√(5/2)r
(¼)r² = √(5/2)r
(1/16)r⁴...
