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Circle/ Ellipse geometry problem from Ramanujan

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Does someone have detail of the problem and his solution? I saw it in youtube. A rough hand sketch remade seeing YouTube video SR geometry problem (17 min 51 sec). I have no access to the TIFR book cited.

G.S.Carr's Book

Thanks in advance.

EDIT1:

The Circle hand drawn by Ramanujan makes it here look like an ellipse due to the lateral perspective of camera. The question title could as well have been "Squaring the Circle Geometry Problem from Ramanujan"

The original image is here :enter image description here

EDIT2:

The picture on the cover of A Synopsis of Elementary results in Pure and Applied mathematics Vol 1 by George Schoobridge Carr ( A century later it was re-issued !) even now has results listed without proofs that attracted Ramanujan's attention. Video 7 min 17 sec.

G.S. Carr's Book (Sad story ... video)


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