Question

can someone help?

Answer 1

The incenters are always inside the triangle. So it's impossible for the incenters to be on the edge of the triangle. Keep in mind that the incircles are always contained in a triangle

http://mathworld.wolfram.com/Incircle.html

Answer 2

The circumcenter will only be on the triangle if and only if the triangle is a right triangle

http://www.regentsprep.org/regents/math/geometry/gc3/AnswerPic3.gif

if the triangle is obtuse, then the circumcenter is outside the triangle

http://jwilson.coe.uga.edu/emat6680/dunbar/assignment4/circumcenter_obtuse.gif

Answer 3

it has to be the circumcentre of a right triangle.

because: A right triangle inscribed within a circle actually forms a diameter with its hypotenuse (better known as a diameter subtends a right angle at the circumference) thus the centre of the circle lies on the hypotenuse of such a triangle