circle problem

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2 total messages Started by Scott Phung Sat, 21 Sep 1996 00:00

#112

Author: Scott Phung
Date: Sat, 21 Sep 1996 00:00

41 lines
1378 bytes

Hi, i'm wondering about the following:

  Given the length of two parallel chords in a circle, and a distance
between them, is there a way to find the length of a middle
parallel chord, that is halfway between the first and second parallel
chord?

  The tough part is that none of these chords are a diameter, so
you don't have a radius to work with.


  To put it another way, let a = 1st chord, b = middle chord, and
c = end chord.		so a > b > c

let's call the difference between a & c, x.
so x/2 would be the difference between a & b, and b & c.

you are given a, c, and x.  Is it possible to find b?

rough diagram:

	----------a-----------  
		  |
		  |
		 x/2
		  |
		  |   
	  --------b--------
		  |
		  |
		 x/2
		  |
		  |
            ------c------

remeber, b is contained inside the circle, as with a and c.
You can use any reasonable value for a, c, and x.

Thanks,
Scott

Re: circle problem

#113

Author: Jeffrey Newmiller
Date: Fri, 27 Sep 1996 00:00

46 lines
2134 bytes

Scott Phung (landmark@vcn.bc.ca) wrote:
: Hi, i'm wondering about the following:
: 
:   Given the length of two parallel chords in a circle, and a distance
: between them, is there a way to find the length of a middle
: parallel chord, that is halfway between the first and second parallel
: chord?
[snip]
: 
: rough diagram:
: 
: 	----------a-----------  
: 		  |
: 		  |
: 		 x/2
: 		  |
: 		  |   
: 	  --------b--------
: 		  |
: 		  |
: 		 x/2
: 		  |
: 		  |
:           ------c------
: 
: remeber, b is contained inside the circle, as with a and c.
: You can use any reasonable value for a, c, and x.

line ac, extended, will bisect the circle.  The endpoints of c, c1 and 
c2, lie on the circle.  one endpoint of a, a1, lies on the circle as well.  
construct a line from c1 to a1, construct bisector of this line, and 
intersection of this bisector with ac will be the center of the circle C 
with radius C-a1. now is easy to find length of line b.

: Thanks,
: Scott

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