To find the length of AB, we can use the tangent-secant theorem. This theorem states that the square of the length of a tangent segment from a point outside the circle (in this case, AB) is equal to the product of the lengths of the entire secant segment and its external part. In our example, we can consider AO as the length from point A to the intersection point with the circle, and BC as a secant line cut off by the points of contact B and C.
Given:
- AO = 30
- BC = 48
According to the theorem:
AB² = AO × BC
Substituting the values we have:
AB² = 30 × 48
AB² = 1440
To find AB, we take the square root of 1440:
AB = √1440
Calculating the square root gives us:
AB ≈ 37.95
Thus, the length of AB is approximately 37.95 units.