Point A is 5 feet from the center of the circle and 12 feet from point B. is tangent to circle O at A. Find OB to the nearest tenth.
To find OB, we can use the properties of tangents and the Pythagorean theorem.
First, let's draw a diagram of the situation. Let O be the center of the circle, A be the point where the tangent line intersects the circle, and B be the other point given.
Since point A is the point of tangency, the tangent line AO is perpendicular to the radius OB.
We are given that OA is 5 feet and AB is 12 feet. We need to find OB.
Using the Pythagorean theorem, we can establish the relationship between OA, OB, and AB:
OA^2 + AB^2 = OB^2
Substituting the given values, we have:
5^2 + 12^2 = OB^2
25 + 144 = OB^2
169 = OB^2
Taking the square root of both sides, we find:
OB ≈ √(169) ≈ 13
Therefore, OB is approximately 13 feet.