posted by Carolina .
Two secants are drawn to a circle from an external point. The external secant length on the first secant is 12 and the internal segment length is 3x +1. The external secant length on the second secant is 15 and the two internal segment length is 3x-1. Solve for (x) to determine the lengths of the two internal segments of the secants.
I assume you meant:
"...and the second internal segment length is 3x-1..."
First, recall that a secant from an external point P cutting a given circle at A and B has the following properties:
PA*PB = PA'*PB' = PT^2....(1)
where A'B' are two other points of intersection of a second secant, and T is the point of tangency.
For the given case,
From equation (1),
3x+1=-17, 3x-1=-19 (impossible).
Unless I made a mistake somewhere, I suggest you recheck the question and proceed to solve for x in the same way above.