stephanieasuquo stephanieasuquo
  • 13-07-2020
  • Mathematics
contestada

Circle A has radius 5, and Circle B has radius 2. If CD = 12 and is a common
tangent, what is AB?

Circle A has radius 5 and Circle B has radius 2 If CD 12 and is a common tangent what is AB class=

Respuesta :

Newton9022 Newton9022
  • 19-07-2020

Answer:

[tex]3\sqrt{17}$ or \approx 12.37$ Units[/tex]

Step-by-step explanation:

In the attached diagram

CA=CO+OA

CO=DB

Therefore:

5=2+OA

OA=3 Units

The angle between a tangent line and a radius is 90 degrees. therefore triangle OAB is a right triangle with:

OB=12 units

OA=3 units

Using Pythagoras theorem

[tex]AB=\sqrt{3^2+12^2}\\ =\sqrt{153}\\=3\sqrt{17}$ or \approx 12.37$ Units[/tex]

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