Given Tangent Line, Find Circle Radius: XY tangent to circle O. If OZ = ZX, XY=6,...

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BigNate

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Oct 2, 2016
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Hello,

I am stuck on #24 in the attached image. Can someone please try to explain this to me? We are told that OZ=ZX and XY = 6 in. I know angle OYX is a right angle making line segment OX the hypotenuse. Given this information, OX should be > 6, but I don't know how to determine that. Then I would need to divide by 2 to get the radius.

If someone could please help me take the next step, that would be much appreciated. Thanks!

Tangent Question.JPG
 
BigNate said:
I am stuck on #24 in the attached image. Can someone please try to explain this to me? We are told that OZ=ZX and XY = 6 in. I know angle OYX is a right angle making line segment OX the hypotenuse. Given this information, OX should be > 6, but I don't know how to determine that. Then I would need to divide by 2 to get the radius.

If someone could please help me take the next step, that would be much appreciated. Thanks!

View attachment 7961
Click to expand...

Let r = the radius

Then:

OY = r
OZ = r
ZX = r

Have you learned the Pythagorean Formula? :cool:
 
Oh, that makes sense now. Thank you both for your hints. Now that you highlight the 30-60-90 triangle, it is very obvious and almost impossible NOT to see it.

I appreciate your time and help!
 
I must be going senile.

How did you guys determine the angles? Is there a rule, regarding the intersection of a circle's tangent line and a radial line?
 
mmm4444bot said:
I must be going senile.

How did you guys determine the angles? Is there a rule, regarding the intersection of a circle's tangent line and a radial line?
Click to expand...
OX/OY = r/(2r) = sin(XOY) = sin(30°)
 
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