Let $OABC$ be a tetrahedron with edges and lateral edges given

Question

Let $OABC$ be a tetrahedron with edges $BC=\sqrt2,CA=\sqrt3,AB=2,OA=\sqrt5,OB=\sqrt6$ and $OC=\sqrt7$.Let $G$ be the centroid of triangle $ABC$ and $M$ and $N$ be the midpoints of $OB$ and $CA$.Find $OG$ and $MN.$

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I could not solve this.I had no idea how i should solve this.Please give me some guidance and help to tackle this question.

Answer 1

1) Use cosine law to find $\angle BAC$.

2) From $\triangle ABN$, find BN. Hence, $NG$ is known.

3) Using the same method, find $ON$.

4) From $\triangle OBN$, find $\angle ONB$.

5) $OG$ can then be found by considering $\triangle ONG$.

That is a start.

PS. Next time, upload a picture to show you have done something.