Since segment AB is tangent to circle O at point B, we know that AB is perpendicular to the radius drawn to point B. This creates a right triangle AOB, where AO is the hypotenuse and r is one of the legs. Using the Pythagorean theorem, we can set up the following equation:
\(r^2 + 9^2 = 12.3^2\)
\(r^2 + 81 = 151.29\)
\(r^2 = 70.29\)
\(r = \sqrt{70.29}\)
\(r ≈ 8.4\)
Therefore, the length of the radius r is approximately 8.4.
Segment AB is tangent to circle O at B. The diagram is not drawn to scale. If AB = 9 and AO = 12.3, what is the length of the radius (r)? Round your answer to the nearest tenth.
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