  We generalize the recent results on radial projections by Orponen, Shmerkin,
Wang using two different methods. In particular, we show that given $X,Y\subset
\mathbb{R}^n$ Borel sets and $X\neq \emptyset$. If $\dim Y \in (k,k+1]$ for
some $k\in \{1,\dots, n-1\}$, then \[ \sup_{x\in X} \dim \pi_x(Y\setminus
\{x\}) \geq \min \{\dim X + \dim Y - k, k\}. \] Our results give a new approach
to solving a conjecture of Lund-Pham-Thu in all dimensions and for all ranges
of $\dim Y$.
  The first of our two methods for proving the above theorem is shorter,
utilizing a result of the first author and Gan. Our second method, though
longer, follows the original methodology of Orponen--Shmerkin--Wang, and
requires a higher dimensional incidence estimate and a dual Furstenberg-set
estimate for lines. These new estimates may be of independent interest.
