Answer:
Length of the segment AC is 27.
Explanation:
Use the Secant-Secant Power Theorem (Intersecting Secants Theorem).
external secant₁ × secant segment₁ = external secant₂ × secant segment₂
External secant is from the vertex to the first point that is intersecting with the circle. Secant segment is the whole line from the vertex to the second point that is intersecting with the circle.
Step 1: Find x.
external secant₁ × secant segment₁ = external secant₂ × secant segment₂
AB × AC = AD × AE
10 × (10 + (x + 6)) = 9 × (9 + (10 + x))
10 × (16 + x) = 9 × (19 + x)
160 + 10x = 171 + 9x
x = 11
Step 2: Find the length of segment AC.
Substitute x with the calculated value.
AC = 10 + x + 6 = 10 + 11 + 6 = 27