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Is segment AB tangent to circle O shown in the diagram, for AB = 10, OB = 5, and AO = 14. Explain your reasoning and show all work in your own words. (The figure is not drawn to scale.)

Is segment AB tangent to circle O shown in the diagram for AB 10 OB 5 and AO 14 Explain your reasoning and show all work in your own words The figure is not dra class=

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If the segment AB is tangent to circle O, then it must be perpendicular to line BO.

Using the pythagorean theorem on the right triangle that we get, the value of AO is the following:

[tex]AO=\sqrt{(10)²+(5)²}=\sqrt{100+25}=\sqrt{125}=11.18[/tex]

we get that AO = 11.18, which is different from the given value 14. Therefore, the segment AB is not a tangent to circle O

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