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 October 8th, 2019, 11:30 AM #1 Newbie   Joined: Sep 2019 From: Fier, Albania Posts: 3 Thanks: 0 find the coordinates of the 2 sides of a chord If I have the circle's equation including r and circle's origin coordinates. And I have the coordinates of a point M in the middle of a chord which splits the chord into 2 equal parts. Then how do I find the coordinates of each point in each side of the chord? October 8th, 2019, 12:18 PM #2 Senior Member   Joined: Jun 2019 From: USA Posts: 310 Thanks: 162 Let $c$ be the half-chord (distance from M to either end of the chord). Let $l$ be the distance between M and the origin O of the circle. Then, by the Pythagorean theorem, $l^2 + c^2 = r^2$. You know $l$ and $r$, so you can find $c$. Now just go $c$ units from M in either direction 90° from segment OM. Hopefully this helped. If not, draw a diagram, and we can walk you through it further. Thanks from tahirimanov19, idontknow and Godhelpme October 9th, 2019, 02:03 AM #3 Senior Member   Joined: Dec 2015 From: somewhere Posts: 734 Thanks: 98 Let the two points be A and B. Try to apply: $\displaystyle d(A,B)=2\cdot d(A,M)=2\cdot d(B,M)$. $\displaystyle d(A,B)$ is the distance between A and B. $\displaystyle d(A,M) \cdot d(M,B) = x(r-x)\:$ , where x is the minimal distance between M and the circle . Now take examples and verify the result you got with a graphing calculator . Last edited by idontknow; October 9th, 2019 at 02:27 AM. Tags chord, coordinates, find, sides Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Shen Geometry 9 April 14th, 2014 01:21 PM adilgrt007 Algebra 9 August 22nd, 2013 10:25 AM Britwells Algebra 3 March 27th, 2013 01:31 PM mathmaniac Algebra 18 March 4th, 2013 05:40 PM mathmaniac Algebra 16 February 14th, 2013 06:27 PM

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