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Inscribed Circle Geometry 
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#1
Jun912, 05:11 PM

P: 116

1. The problem statement, all variables and given/known data
Find the radius of a circle inscribed in a quadrant of a circle with radius 5 2. Relevant equations 3. The attempt at a solution I worked this but I'm not sure if its correct. I looked at the first quadrant so a quarter of a circle with radius 5. I drew the radius that would bisect the angle at the origin into 45° angles. I found the midpoint of the radius and dropped a line to the xaxis from that midpoint. This forms a 454590 triangle which would make the radius of the inscribed circle 2.5/√2. Is this correct?? 


#2
Jun912, 05:32 PM

P: 294

Your method seems correct, but I got [itex]\frac{5}{1+\sqrt{2}}[/itex].
Is it possible you can show a picture of where you are making your triangle? 


#3
Jun912, 05:49 PM

P: 116




#4
Jun912, 05:58 PM

P: 294

Inscribed Circle Geometry
Is the center circle here the one you are trying to find the radius of?



#5
Jun912, 06:02 PM

P: 116




#6
Jun912, 06:09 PM

P: 294

The problem with your work I think was assuming that the line dropped down from the center of that circle bisected the bottom line, which isn't true.



#7
Jun912, 06:11 PM

P: 116




#8
Jun912, 06:14 PM

P: 294

Oh oh oh, I see now. But if that were true, then wouldnt the radius also have to be 2.5? Since the segment from the center to the outside of the larger circle is 2.5 and that is another radius of the circle.



#9
Jun912, 06:21 PM

P: 116




#10
Jun912, 06:26 PM

P: 294

If it helps, I used the diagonal line in order to solve for the radius.
I don't want to say too much however. 


#11
Jun912, 06:34 PM

P: 116




#12
Jun912, 06:36 PM

P: 294

Yeah, the one that is 45 degrees above the horizontal.



#13
Jun912, 06:39 PM

P: 116

I'm assuming you didn't use 2.5,2.5 as your center??



#14
Jun912, 06:42 PM

P: 294

Right.
What is the length of that segment? How can you label its parts in terms of r? 


#15
Jun912, 06:46 PM

P: 116

I'm not sure I need to look at it some more :(



#16
Jun912, 06:54 PM

P: 116

Ok now I got (10√2)/4 its close to your answer but still not the same. I need to go back and see if I made a calculation error.



#17
Jun912, 06:56 PM

P: 294

Explain how you got to that.



#18
Jun912, 07:04 PM

P: 116

Its wrong I was assuming that perpendicular segment was the radius of the inscribed circle. I need to add 2.5 to that piece that I keep thinking is a radius (but not) to get the diameter but I don't know how to get it



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