Question 895788
One of the radii of the circle has an endpoint meeting the line 4x+3y=10 at a right angle.  The LINE for this radius has slope {{{-3/4}}} and contains the point (0,0).  I identified this slope through using an understanding of the standard form in which the line 4x+3y=10 was given.


Can you derive the equation of the line containing this radius which meets 4x+3y=10 at a right angle?  When you do, then you have two equations of intersecting lines; and you can find the intersection point.


Once that is done, you have this endpoint and the other end point, (0,0), which form the perpendicular radius.  Use Distance Formula to find and compute the value of the radius.


Can you do that, and then finish?