Question

AB is tangent to circle O at B. Find the length of the radius (r) for AB = 6 and AO = 11.7. Round to the nearest tenth if necessary. The diagram is not to scale.

Answer 1

10.0

Explanation:

`AO^(2) = r^(2) + AB^(2) \\11.7^(2) = r^(2) + 6^(2) \\136.89 = r^(2) + 36\\\\136.89 - 36 = r^(2) + 36 - 36\\r^(2) = 100.89\\r = √(100.89) \\r = 10.0`

Answer 2

Connecting all the end points of the segments will form a right triangle with one leg equal to AB = 6. Its hypotenuse is AO = 11.7. From the Pythagorean theorem,
(AO)² = (AB)² + (BO)²
where BO is the radius (r). Substituting the values,
11.7² = 6² + r²
The value of r is approximately 10.0