The standard form of a line is in the form

A, B and C are integers, and A is positive. Let's start with multiplying the whole equation by 3 to get rid of denominators:

Subtract 3y from both sides:

Which of course is equivalent to

Which is the standard form, given the coefficients A=1, B=-3, C=6.
Where the angle bisectors intersect determines the center of the incircle.
Where the side perpendicular bisectors intersect determines the center of the center of the circumcircle. From these definitions, you should be able to determine the points you want.
Answer:
Step-by-step explanation: