Circle Chord Length

Question

Say I have a circle on a grid, and that the center of the circle is at the origin. And say that the circle has a radius of 5. How would I find the width of the circle along the x-axis if I have a certain position along the y-axis?

Answer 1

Draw a right triangle.  If you have the position on the y-axis, then let that position be y, and let the width on the x-axis be x.  Since the radius is 5, the equation of the circle is:

 

x² + y² = r²

 

x² + y² = 25

 

x² = 25 - y²

 

x = sqrt(25-y²)

 

If you plug in the number for y, then you can solve for x given the above equation.

 

Hope this helps!