The problem is illustrated by the figure shown below.
It is clear that ΔABC is a right triangle because
(a) it is inscribed in a circle,
(b) Its sides satisfy the Pythagorean theorem because
6² + 8² = 36 + 64 = 100, and 10² = 100.
Therefore, AC is the diameter of the circumscribing circle, and the radius is
r = 5.
The area of the circumscribing circle is
A₁ = π(5²) = 25π
The area of the triangle is
A₂ = (1/2) 8*6 = 24
The required area, of the circumcircle minus that of the triangle (shaded area) is
A₁ - A₂ = 25π - 24 = 54.54 square units.
Answer:
54.54 square units.
