Given that AB is a tangent of the circle with the center at X, AB = 12, and XD = 2.5, which is the length of DB

No idea where A and B are on that tangent.

No idea where D is

To find the length of DB, we need to apply the tangent line theorem. According to this theorem, if a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.

In this case, AB is a tangent of the circle, and X is the center of the circle. So, we can draw the radius XD from the center X to the point of tangency D.

Since AB is perpendicular to XD, we can form a right triangle AXD, where AD is the hypotenuse, XD is one leg, and AD - XD (which is DB) is the other leg.

Now, we have XD = 2.5 and AB = 12. We need to find DB.

To find DB, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (AD) is equal to the sum of the squares of the lengths of the other two sides (XD and DB).

In this case, we have:

AD^2 = XD^2 + DB^2

(AD - XD)^2 = XD^2 + DB^2 (since AD - XD is equal to DB)

Using the given values, we can substitute XD = 2.5 into the equation:

(AD - 2.5)^2 = 2.5^2 + DB^2

Simplifying further:

AD^2 - 5AD + 6.25 = 6.25 + DB^2

AD^2 - 5AD = DB^2

Now, we need additional information to solve for DB. Please provide the length of AD or any other relevant information available.