Consider this figure [img]: how many points $D$ are there such that $\alpha=90°$? * $j, f$ and $g$ are of arbitrary length but orthogonal to each other ($j$ and $g$ are parallel) * the lines $i$ and $h$ are simply connected to $D$, not reflected therein How many different spots exist for $D$, so that $i$ and $h$ are orthogonal as well ($\alpha=90°$)? ![enter image description here]( From playing around with GeoGebra, it looks like there are $0, 1$ or $2$, depending on the lengths of $j$ and $g$ – how do I prove that in a general fashion?

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After constructing the semicircle EDC using EC as diameter, we can slide C along the vertical line through B. This shows there are 0, 1, 2 possible solutions. It is just the discussion of how many ways that a line cuts a circle.

Also, there is an extreme case:- when g = 0.