Y coordinates of points on circumference given segment height and circle center coordinates

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A month ago I've posted this question, now I realized that there are some problems with y coordinates.

This is the problem. I have a circle with center at (cx, cy) and the heights hA, hB, hC, hD of the circular segments A, B, C and D. I would like to find the coordinates of the points a, b, c, d, ... , k.

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The problem is the y coordinates of those points. How can I compute them?

The user Gribouillis answers that a generic point on circumference has coordinates $(x, y) = (x, c_y + r - h)$ but I don't think that $c_y + r -h$ is right.