Question 1110106
You can make a sketched graph for this circle, center at the point (0,0). 

If you make AB and CD segments (chords) perpendicular to y-axis and for convenience, above the x-axis, then you can identify  two points on the circle and you know x coordinates but you can find the y-coordinates.


You can start the circle's equation as  {{{x^2+y^2=13^2}}}


Half of AB is {{{24/2=12}}} so here, x=12.
{{{x^2+y^2=169}}}
{{{y^2=169-x^2}}}
{{{y=sqrt(169-x^2}}}
{{{y=sqrt(169-144)}}}
{{{highlight(y=5)}}}



Half of CD is {{{10/2=5}}}, so here, x=5.
{{{y=sqrt(169-25)}}}
{{{highlight(y=12)}}}


In the described arrangement, chord AB is 5 units from the center, and chord CD is 12 units from the center, both chords perpendicular to the positive y-axis.  SEVEN units apart from each other;  12-5=7.



(You can do a similar arrangement but put the two parallel chords on OPPOSITE sides of the origin, and may get a different distance between chords.)