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We measure the absolute frequency of seven out of the nine allowedtransitions between the 2$^3${\it S} and 2$^3${\it P} hyperfine manifolds in ametastable $^3$He beam by using an optical frequency comb synthesizer-assistedspectrometer. The relative uncertainty of our measurements ranges from $1\times10^{-11}$ to $5\times 10^{-12}$, which is, to our knowledge, the most preciseresult for any optical $^3$He transition to date. The resulting $2^3${\itP}-2$^3${\it S} centroid frequency is $276\,702\,827\,204.8\,(2.4)$kHz.Comparing this value with the known result for the $^4$He centroid andperforming {\em ab initio} QED calculations of the $^4$He-$^3$He isotope shift,we extract the difference of the squared nuclear charge radii $\delta r^2$ of$^3$He and $^4$He. Our result for $\delta r^2=1.074 (3)$ fm$^2$ disagrees byabout $4\,\sigma$ with the recent determination [R. van Rooij {\em et al.},Science {\bf 333}, 196 (2011)].

Frequency metrology of helium around 1083 nm and determination of the nuclear charge radius