P5008 Sun 2022-07-31 20:15:29 link reply 0252b9f840be859b37c023adc421d512cf25176b5ca40ebb32046d2e079855c3.png 198 KiB 3000x3927 In the case of the square (of side L to make it easy) existing, there is of course the 1:2 similarity between triangles ABC and QPC (since QP and RS and therefore AB are parallel and QC lies on AC and PC lies on BC), so |AB|=2|QP|=2L. And as |QR|=L, |CH|=2L with H as described by P4990 . So ABC must always have an area of 4L^2. Expressing |AC|...

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