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1 AB is tangent to circle O at B. The diagram is not drawn to scale. If AB=12 nd AO=15, what is the length of the radius (r)

1 AB is tangent to circle O at B The diagram is not drawn to scale If AB12 nd AO15 what is the length of the radius r class=

Respuesta :

Answer:

r = 9 units

Step-by-step explanation:

since AB is a tangent to the circle at B , then ∠ ABO = 90°

so Δ ABO is a right triangle

using Pythagoras' identity in the right triangle

OB² + AB² = AO² , that is

r² + 12² = 15²

r² + 144 = 225 ( subtract 144 from both sides )

r² = 81 ( take square root of both sides )

r = [tex]\sqrt{81}[/tex] = 9

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