18 a line
19 one plane
17. one, and only one
18. a line
19. one and only one plane
it’s the 2nd, 3rd and 5th one
I believe it is 3 non-collinear points.
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.
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
A plane is a flat 2D surface. It is a rule that you need at least 3 points to know the orientation (angle) of the plane. Two points would only be able to form a line, and though that line can be going through the plane, you won't be able to know what orientation (angle) that plane is at.