Given a circle (for simplicity, $x^2 + y^2 = 1$) and a chord on this circle parallel to the $x$ axis $y = p - 0.5$ ($p \in [0,1]$ being the only parameter I control), how can I estimate the relationship between $p$ and the ratio between the circular segment determined by the circle and the chord and the point $(0,-1)$?
I do not require full precision (I only have coarse control over $p$, after all), but if no readily available approximation is available, I'll take the full formula.
In English — I have a circular shape in Powerpoint; I want to color a portion of its area with a given color. Powerpoint doesn't let me color a circular sector using the gradient fill tool, so I have to resort to a gradient section. The alternative is complicating the drawing with the arc tool and its fiddly controls. Thus, I'd like to know what portion of the circle I'd color if I color what's below a chord placed at $p$% height of the circle with red and the remainder in white.