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?
where is D ?
To find the length of DB, we can use the properties of a tangent to a circle.
First, let's understand the situation. We have a circle with its center at X, and AB is a line tangent to the circle. The point of tangency is the point where AB touches the circle and is perpendicular to the circle's radius, which passes through that point. In this case, let's assume that D is the point of tangency between the circle and AB.
Now, we have some given information. AB is 12 units long, and XD is 2.5 units long.
To find the length of DB, we need to use the fact that the tangent to a circle is perpendicular to the radius at the point of tangency. In this case, DB is a radius of the circle, and AD is perpendicular to AB.
Since AB is a tangent to the circle, we can draw a right triangle in which AD is the height, DB is the base, and AB is the hypotenuse.
Using the Pythagorean theorem, we have:
AB^2 = AD^2 + DB^2
Plugging in the given values, we get:
12^2 = (2.5)^2 + DB^2
Simplifying:
144 = 6.25 + DB^2
Subtracting 6.25 from both sides:
137.75 = DB^2
To solve for DB, we can take the square root of both sides:
DB = √(137.75)
Using a calculator, we find DB ≈ 11.73.
Therefore, the length of DB is approximately 11.73 units.