Question

which best explains why the orthocenter of an obtuse triangle is outside the triangle?
all three of the altitudes lie entirely outside the triangle
two of the altitudes lie entirely outside the triangle
all three of the medians lie entirely outside the triangle
two of the medians lie entirely outside the triangle

Explanation:

The orthocenter is the intersection of a triangle's altitudes. In an obtuse triangle, two altitudes extend outside the triangle. This causes their intersection (the orthocenter) to be outside. Medians always lie inside the triangle, so options involving medians (C and D) are incorrect. Option A is wrong as only two altitudes (not all three) are outside in an obtuse triangle.

Answer:

B. Two of the altitudes lie entirely outside the triangle