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Inscribed Circle Geometry

by Wildcat
Tags: circle, geometry, inscribed
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Wildcat
#1
Jun9-12, 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 x-axis from that midpoint. This forms a 45-45-90 triangle which would make the radius of the inscribed circle 2.5/√2. Is this correct??
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Villyer
#2
Jun9-12, 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?
Wildcat
#3
Jun9-12, 05:49 PM
P: 116
Quote Quote by Villyer View Post
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?
I am looking at the first quadrant. Center of the circle with radius 5 is at the origin, so I draw my radius from the origin and bisecting the 90 angle. Then from the midpoint of that radius (2.5)(which I think will be the center of the inscribed circle) I drop the segment to the x-axis which will be a leg of the 45-45-90 and also the radius of the inscribed circle.?? so the triangle has a hypotenuse of 2.5 and dividing by √2 would be the leg/radius ??

Villyer
#4
Jun9-12, 05:58 PM
P: 294
Inscribed Circle Geometry

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

Wildcat
#5
Jun9-12, 06:02 PM
P: 116
Quote Quote by Villyer View Post
Is the center circle here the one you are trying to find the radius of?

Yes! I love the drawing!
Villyer
#6
Jun9-12, 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.
Wildcat
#7
Jun9-12, 06:11 PM
P: 116
Quote Quote by Villyer View Post
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.
No I wasn't assuming that. The first part of the bottom line would be 2.5/√2 as well since the triangle formed is a 45-45-90.
Villyer
#8
Jun9-12, 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.
Wildcat
#9
Jun9-12, 06:21 PM
P: 116
Quote Quote by Villyer View Post
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.
I don't think the midpoint of the 5 radius is the center of the inscribed circle anymore because you are correct about the 2.5 but the perpendicular line would also have to be a radius and it is 2.5√2 so that must not be the center
Villyer
#10
Jun9-12, 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.
Wildcat
#11
Jun9-12, 06:34 PM
P: 116
Quote Quote by Villyer View Post
If it helps, I used the diagonal line in order to solve for the radius.

I don't want to say too much however.
Are you talking about the radius drawn in that bisects the 90 at the origin??
Villyer
#12
Jun9-12, 06:36 PM
P: 294
Yeah, the one that is 45 degrees above the horizontal.
Wildcat
#13
Jun9-12, 06:39 PM
P: 116
I'm assuming you didn't use 2.5,2.5 as your center??
Villyer
#14
Jun9-12, 06:42 PM
P: 294
Right.

What is the length of that segment? How can you label its parts in terms of r?
Wildcat
#15
Jun9-12, 06:46 PM
P: 116
I'm not sure I need to look at it some more :(
Wildcat
#16
Jun9-12, 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.
Villyer
#17
Jun9-12, 06:56 PM
P: 294
Explain how you got to that.
Wildcat
#18
Jun9-12, 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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