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

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

Answer 2

Answer:

10.0

Step-by-step explanation:

$AO^{2} = r^{2} + AB^{2} \\11.7^{2} = r^{2} + 6^{2} \\136.89 = r^{2} + 36\\\\136.89 - 36 = r^{2} + 36 - 36\\r^{2} = 100.89\\r = \sqrt{100.89} \\r = 10.0$