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 January 5th, 2012, 03:47 PM #1 Newbie   Joined: Jan 2012 Posts: 28 Thanks: 0 Find the number of chords A chord of length 16 is perpendicular to a diameter at point A. If the circle's diameter is 30, find the number of chords of integral length (other than the diameter) that contain A. January 5th, 2012, 07:49 PM #2 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs Re: Find the number of chords Using coordinate geometry, where the center of the circle is at the origin, the circle is given by: Taking point A as (A,0) where 0 < A we set: The family of lines passing through A is: where to exclude the diameter. So we then substitute for y into the circle's equation: So we then require: where and 2n is the chord length. In order for m to be real and non-zero, we require: We find and for each n there are two chords for the two roots of m, and adding the given vertical chord makes a total of: 2(30 - 17) + 1 = 27 chords passing through A of integral length, excluding the diameter, represented by n = 15 and m = 0. In retrospect, the answer seems so obvious now.  January 6th, 2012, 05:39 PM #3 Newbie   Joined: Jan 2012 Posts: 28 Thanks: 0 Re: Find the number of chords Thanks for your try but the answer is only between 26 and 1. I hope you can explain it to me. Thanks January 6th, 2012, 06:15 PM #4 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs Re: Find the number of chords Perhaps they are also excluding the given chord as well as the diameter? edit: I notice on another forum the length of the vertical chord is given as 18...which is it, 16 or 18? January 6th, 2012, 08:29 PM #5 Newbie   Joined: Jan 2012 Posts: 28 Thanks: 0 Re: Find the number of chords It was my mistake that it is 18 . Thanks I didn't notice that too. January 6th, 2012, 08:30 PM #6 Newbie   Joined: Jan 2012 Posts: 28 Thanks: 0 Re: Find the number of chords Can you show how your solve this again with 18 instead of 16. Thanks January 6th, 2012, 08:42 PM #7 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs Re: Find the number of chords If we exclude the given chord (minimum length) and the diameter (maximum length) then we have 2 chords of length {19, 20,...28,29} = 22 chords. January 7th, 2012, 07:26 AM #8 Newbie   Joined: Jan 2012 Posts: 28 Thanks: 0 Re: Find the number of chords The number of chords of integral length (other than the diameter) that contain A is 22?? Tags chords, find, number ### number of chords in a circle with integral length

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