Circle, triangle
Level
pending
A circle of radius 4units circumscribes a triangle whose area is 8 square units.Find the product of the sides of the triangle.
64
128
74
96
56
132
112
32
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1 solution
Let a , b , c denote the side lengths of the triangle, and R denote the circumradius. Law of signs tells us a / s i n ( A ) = 2 R .
Also A r e a = 2 1 b c s i n ( A ) .
Rearranging gives A r e a = 4 R a b c .
Plugging in the numbers gives us a b c = 1 2 8