If A(5,2),B(10,12) and P(x,y) is such that APPB=32 ,  then the internal bisector of ∠APB always passes through

Let internal bisector of ∠APB meets the side AB at C .  We know that ACBC=APPB∴ ACBC=32∴ coordinates of C are 3(10)+2(5)3+2,3(12)+2(2)3+2 or (8,8) Hence the internal bisector of ∠APB always passes through  point (8,8)