Answer:
10
Step-by-step explanation:
The radius is the magnitude of the complex number that is the difference between any point on the circle and the center point. A suitable calculator can tell you that magnitude:
║(8+7i) - (2-i)║ = √((8-2)² +(7-(-1))²) = √(36+64) = √100 = 10
Since O is inscribed in triangle ABC, you know that AB, AC, and BC are all tangent to the circle. The tangent segments theorem asserts that AD is congruent to A F; BD is congruent to BE; and CF is congruent to CE. (NOTE: E is the point where the circle touches BC - I've taken the liberty of labeling it as such.)
Then the perimeter of triangle ABC will be twice the sum of the labeled edges: