Answer
which of the following statements are correct? select all that apply.
-- only two of three angle bisectors of the internal angles of a triangle are concurrent.
-- the circumcenter of a triangle is the point where the perpendicular bisectors of the sides meet.
-- given any three non-collinear points, there exists exactly one circle that passes through the points.
-- a circumscribed circle is the circle that passes through all three vertices of a triangle and it is the smallest triangle contained within any triangle.
-- the incenter of a triangle is the point where the angle bisectors meet.

it’s the 2nd, 3rd and 5th one

Step-by-step explanation:

Given are some properties of triangles and we have to check whether they are correct

i) Only two of three angle bisectors of the internal angles of a triangle are concurrent.

This is incorrect since all three angle bisectors concur at incentre

ii) The circumcenter of a triangle is the point where the perpendicular bisectors of the sides meet.

-- correct because the meeting point is equidistant from all three vertices

iii) Given any three non-collinear points, there exists exactly one circle that passes through the points.

-- correct because any three points determine a circle

iv) Given any three non-collinear points, there exists exactly one circle that passes through the points.

-- Correct

v) The incenter of a triangle is the point where the angle bisectors meet.

-- Correct and the centre is equidistant from the sides of the triangle

452,489 to the nearest thousand is 452,000