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2 problems match “perpendicular bisector”. Clear

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1. Center of a circle through three points ●●○○○ 20 ptsA circle passes through the points $(-1, 2)$, $(3,0)$ and $(9,0)$. The center of the circle is at $(h,k)$. Find the value of $h+k$.
2. Edge length of a cube from distances ●●●○○ 50 ptsLet $P$ be a point inside the cube $ABCD\text{-}EFGH$, where $ABCD$ and $EFGH$ are opposite faces and $E,F,G,H$ lie directly above $A,B,C,D$ respectively. Given $PA=PB=\frac{3\sqrt{3}}{2}$ and $PF=PC=\frac{\sqrt{107}}{2}$, find the edge length of the cube.