Answer:
x = 15, AC = 25
Step-by-step explanation:
Given a tangent and a secant from a external point to a circle, then
The product of the external part and the whole of the secant is equal to the square of the tangent.
(9)
12(12 + x) = 18² = 324 ( divide both sides by 12 )
12 + x = 27 ( subtract 12 from both sides )
x = 15
(10)
9(9 + 3x + 1) = 15²
9(3x + 10) = 225 ( divide both sides by 9 )
3x + 10 = 25 ( subtract 10 from both sides )
3x = 15 ( divide both sides by 3 )
x = 5
Then
AC = 3x + 10 = 3(5) + 10 = 15 + 10 = 25
