Mathematics Question and Solution
Calculating length AK.
Notice.
CM = 64/17 units.
AB = AD = BC = CD = 8 units.
r is the radius of the circle.
a²+(64/17)² = 8²
a² = 64-(4096/289)
a² = 14400/289
a = √(14400/289)
a = 120/17 units.
a is BM.
b = 2r units.
Calculating r.
a ~ 2r
(64/17) ~ 8
It implies;
(120/17) ~ 2r
(64/17) ~ 8
Therefore;
15 ~ r
8 ~ 4
Cross Multiply.
8r = 4*15
r = ½(15) units.
r = 7.5 units.
Again, r is the radius of the circle.
Or
(64/17) ~ (120/17)
8 ~ 2r
Cross Multiply.
2r(64/17) = 8(120/17)
2r*64 = 8*120
64r = 4*120
16r = 120
2r = 15
r = 7.5 units.
c = 8+r
c = 8+½(15)
c = 15.5 units.
Calculating length AK, let it be x.
x²+7.5² = 15.5²
x² = 15.5²-7.5²
x = √(15.5²-7.5²)
x = 2√(46) units.
x = 13.5646599663 units.
Again, x is length AK.
