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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 halfchord (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. 
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. $\displaystyle d(A,M) \cdot d(M,B) = x(rx)\:$ , 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. 

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chord, coordinates, find, sides 
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