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.
Answer Choices:
13 ft
14.3 ft
26 ft
5 ft
To find OB, we can use the properties of a tangent line to a circle.
First, let's draw a diagram to visualize the problem. Let O be the center of the circle, and let A and B be the given points. We are looking for the length OB.
Since A is a tangent to the circle, the radius of the circle must be perpendicular to it. Let's draw the radius OC from the center O to the point of tangency A.
Next, we can create a right triangle OAB. The given information tells us that OA is 5 feet and AB is 12 feet. We want to find OB.
Using the Pythagorean theorem, we can find the length of OB. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, OB is the hypotenuse, and OA and AB are the other two sides. So we have the equation OA^2 + AB^2 = OB^2.
Substituting the known values, we get:
5^2 + 12^2 = OB^2
25 + 144 = OB^2
169 = OB^2
So OB is the square root of 169, which is 13.
Therefore, the nearest tenth of OB is 13 feet.