Yes
Yes
Two points. These may coincide if the line is a tangent to the sphere.
The answer will depend on how the triangle is situated within the rectangle (how many of the triangle's vertices coincide with those of the rectangle), and what other information you have.
If the lines intersect, then the intersection point is the solution of the system. If the lines coincide, then there are infinite number of the solutions for the system. If the lines are parallel, there is no solution for the system.
yes the centroid of the rectangle coincide with the intersection of the diagonals with the center of mass
Yes
Yes
A triangle has only one centroid (so not centroids) and it is the intersection of its medians by definition.A triangle has only one centroid (so not centroids) and it is the intersection of its medians by definition.A triangle has only one centroid (so not centroids) and it is the intersection of its medians by definition.A triangle has only one centroid (so not centroids) and it is the intersection of its medians by definition.
Two points. These may coincide if the line is a tangent to the sphere.
The answer will depend on how the triangle is situated within the rectangle (how many of the triangle's vertices coincide with those of the rectangle), and what other information you have.
yes because is has 3 sides and all of the corners intersect
yes because is has 3 sides and all of the corners intersect
yes because is has 3 sides and all of the corners intersect
Yes. The orthocenter is the intersection of the altitudes; the circumcenter is the intersection of the perpendicular bisectors of the three sides of the triangle. The perpendicular bisector of and altitude to a given side are parallel, so they can coincide at the common center only if they are the same; that means that the opposite vertex is on the perpendicular bisector, so the other two sides are equal. Thus each pair of sides are equal, so the triangle is equilateral.
Main Street and Highway 70 coincide in the downtown area but diverge after the intersection with Morris Street.
If the lines intersect, then the intersection point is the solution of the system. If the lines coincide, then there are infinite number of the solutions for the system. If the lines are parallel, there is no solution for the system.