I wanted to know if there is a way to calculate a chord that spans a circle, perpendicular to the origin point of the circle. In the image below, I need a way to calculate the length of the blue line that intersects the green dot perpendicular to the origin point of the circle. The red line is just to illustrate what I mean by perpendicular to the origin. For this problem, I know the coordinates of the green dot, and the coordinates of the focal point of the circle (0,0). Thanks in advance!
2026-04-03 18:13:05.1775239985
Is it possible to calculate a chord perpendicular to the focal point of a circle?
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Hint: Let $AB$ be the chord, $D$ be the green dot and $O$ be the origin (as well as the center of the circle). Then you can calculate the length of $OD$ since you know their coordinates. Furthermore, $OA$ and $OB$ are just the radii of the circle, and you get the answer by the Pythagorean theorem easily from here.