This very attractive geometrical puzzle is from Catriona Agg. It looks like there isn't enough information, although there is. See the Comments for my solution.
![](https://learn1.open.ac.uk/mod/oublog/pluginfile.php/15/mod_oublog/message/236344/purple-sun-question.jpg)
But even after solving it it still feels as though there is an information deficit somewhere!
Comments
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Here's my take on it.
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I arrived at 36 π by minimising the circle so ending up with the horizontal line being the radius of the purple quarter circle. So area = π (12)2 / 4 = 36 π. More of an intuitive solution than a rigorous proof.
Jan