Mathematics Question and Solution
Let a be the radius of the circle.
It implies;
a² = 16²+b²-2*16bcos45
a² = 256+b²-16√(2)b --- (1).
a² = 8²+b²-2*8bcos135
a² = 64+b²+8√(2)b --- (2).
Equating (1) and (2) to get b.
256+b²-16√(2)b = 64+b²+8√(2)b
192 = 24√(2)b
8 = √(2)b
b = 4√(2) units.
b = 5.6568542495 units.
Calculating a, radius of the circle.
Recall.
a² = 256+b²-16√(2)b at (1).
And b = 4√(2) units.
a² = 256+(4√(2))²-16√(2)*4√(2)
a² = 256+32-128
a² = 288-128
a² = 160
a = √(160)
a = 4√(10) units.
a = 12.6491106407 units.
Again, a is the radius of the circle.
