area of region in which point $P$ can move such that $\angle APB\geq 60^\circ$

Question

if $A(2,-6)$ and $B(8,2)$ are two fixed points , Then find area of region in which point $P$

can move such that $\angle APB\geq 60^\circ$

wan,t be able how to start, help me

Answer 1

Ignoring coodinates for now, we have that $\angle ABC=c$ (for some constant $c$, $A,B$ fixed) iff $P$ lies on one of the circular arcs:

So we have that P must lie within the arcs, i.e in the shaded region.