F.3 Maths

Let P be (x , 0).
It must be x < 5 , otherwise
PA + PB + PC > PA + PB > CA + CB = √((5-1)² + (0-5)²) + √((5-2)² + (0+1)²) = 9.56...> 9.
PA + PB + PC < 9
√( (x-1)² + (0-5)² ) + √( (x-2)² + (0+1)² ) + √( (x-5)² + (0-0)² ) < 9
√( (x-1)² + 25 ) + √( (x-2)² + 1 ) + 5 - x < 9 ..... since x < 5
√( (x-1)² + 25 ) + √( (x-2)² + 1 ) - x < 4When x = 4 ,
√( (4-1)² + 25 ) + √( (4-2)² + 1 ) - 4 = 4.067... > 4 , rejected.When x = 3 ,
√( (3-1)² + 25 ) + √( (3-2)² + 1 ) - 3 = 3.799378... < 4 .Suggested P(3 , 0).