please help !! thanks in advance :D

[tex]CIRCLES[/tex]

◆ A little manipulation of the diagram
( as shown in the attachment )

Once you're done with this simple manipulation and the labeling, we get the equation : OB² + BC² = OC²

• r² = ( r - 9 )² + 15²

Solve this trivial equation to get : r = 17

• Radius = 17 is your final answer .
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Hope this helps you :)

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gmany gmany · Answer 2 · 2019-08-18T15:44:44+02:00

Answer:

a) 17

Step-by-step explanation:

Look at the picture.

We have the right triangle (red). Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have

[tex]leg=15,\ leg=r-9,\ hypotenuse=r[/tex]

Substitute:

[tex]15^2+(r-9)^2=r^2[/tex] use (a - b)² = a² - 2ab + b²

[tex]225+r^2-2(r)(9)+9^2=r^2[/tex]

[tex]225+r^2-18r+81=r^2[/tex] subtract r² from both sides

[tex]306-18r=0[/tex] subtract 306 from both sides

[tex]-18r=-306[/tex] divide both sides by (-18)

[tex]r=17[/tex]