Find the area of the portion of the circle that is outside triangle RST if the radius of the circle is 8 cm

From my research, it was shown that angle T had a value of 60 degrees, while angle S had a value of 70 degrees. Triangle RST in inscribed in the circle, so obtaining the areas of both shapes and subtracting one from the other would yield the area being looked for.

To obtain the area of triangle RST, it is necessary to obtain the values of its sides first. The sides can be obtained using the sine law, as shown below:

(a / sin A) = (b / sin B) = (c / sin C) = 2R

Similarly:

(r / sin 50) = (s / sin 70) = (t / sin 60) = 2 (8)

Therefore:

r = 6.128

s = 7.518

t = 6.928

Obtaining the area of the triangle:

A = (rst) / 4R

A = 9.97 cm^2

Obtaining the area of the circle:

A = pi*r^2

A = 201.06 cm^2

Therefore, the area of the portion is equal to 201.06 - 9.97 = 191.09 cm^2