The points of intersection of the purple and green circles line up with the points of intersection of the green and orange, lines meeting on the orange circle. Show that the circle centers plus the orange point form a parallelogram.
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Solution
Observe that the distance between the peaks, in the direction of AB, is just half the distance between A and B, leading to the result.
Apply this lemma twice to show that the purple centre is the parallelogram vertex.
More solutions: https://x.com/Mirangu1/status/1875111836770848798
One reply on “Monolith among the moons”
The last two drawings in the Solution were kindly provided by @steph_bernard69. Thank you!