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Problem:

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I have got so far that the radius of the small semi-circle + the radius of the larger semi circle is 2. I'm not sure how to proceed, however...

Any help?

Edit:

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Let the larger semicircle have radius $r$. We see that, since it's angled at $45^\circ$, $$r+\frac{\sqrt2}2r=2\implies r=\frac2{1+\sqrt2/2}=4(1-\sqrt2/2)$$ From here you should be able to work out the solution, since you know the sum of the semicircle radii.

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  • $\begingroup$ thank you - however: please could you clarify where you got the value of frac\{sqrt2}{2} - it might be me being thick, but unfortunately, I don't follow... $\endgroup$
    – vgupt
    Oct 22, 2020 at 15:40
  • $\begingroup$ Draw a vertical segment through common center and parallel to side of square. Upper segment is radius of smaller semicircle. Lower segment is radius of larger semicircle. $\endgroup$
    – cosmo5
    Oct 22, 2020 at 15:52
  • $\begingroup$ @cosmo5 - but why is the lower segment equal to sqrt2/2 * the radius of the smaller semi circle $\endgroup$
    – vgupt
    Oct 22, 2020 at 16:13
  • $\begingroup$ Thanks @ParclyTaxel $\endgroup$
    – vgupt
    Oct 22, 2020 at 16:20
  • $\begingroup$ But @ParclyTaxel - how do you know that the segment from the common centre to the south west point of the larger semi circle is equal to the vertical segment of the isosceles triangle? $\endgroup$
    – vgupt
    Oct 22, 2020 at 16:21

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