Mathematics Question and Solution
Let a be the radius of the circle.
a² = 6²+8²+2*6*8cosb
a² = 100+96cosb --- (1).
a² = 16²+8²-2*16*8cosb
a² = 320-256cosb --- (2).
Equating (1) and (2).
100+96cosb = 320-256cosb
cosb = 220/352
b = 51.3178125465°
It implies, using (2).
a² = 320-256cos51.3178125465
a = 12.6491106407 units.
Again, a is the radius of the circle.
Therefore, area of the circle is;
πa²
= π(12.6491106407)²
= 160π square units.
