Mathematics Question and Solution
Let a be the radius of the circle.
c = (a-1) units.
Calculating a.
7² = a²+(a-1)²-2a(a-1)cosb
49 = a²+a²-2a+1-(2a²-2a)cosb
48 = 2a²-2a-(2a²-2a)cosb
(2a²-2a)cosb = 2a²-2a-48 --- (1).
11² = a²+(a-1)²-2a(a-1)cosb
121 = a²+a²-2a+1-(2a²-2a)cosb
120 = 2a²-2a+(2a²-2a)cosb
(2a²-2a)cosb = 120+2a-2a² --- (2).
Equating (1) and (2).
2a²-2a-48 = 120+2a-2a²
4a²-4a-168 = 0
a²-a-42 = 0
a²-7a+6a-42 = 0
a(a-7)+6(a-7) = 0
(a-7)(a+6) = 0
Therefore;
a = 7 units.
Again, a is the radius of the circle.
The circumference of the circle is;
2πa
= 2*π*7
= 14π units.
