Question

In geometry, if a triangle has an obtuse angle, what can be said about its orthocenter's position relative to the triangle?

A) Inside the triangle
B) Outside the triangle
C) At the centroid of the triangle
D) On one of the triangle's sides

Answer 1

In geometry, the orthocenter of a triangle with an obtuse angle is located outside of the triangle, as the altitudes from the acute angles extend beyond the triangle to intersect. the correct option is: B) Outside the triangle.

Step-by-step explanation:

In geometry, when dealing with triangles, an important concept to understand is the orthocenter. The orthocenter of a triangle is the point where the triangle's three altitudes intersect. An altitude of a triangle is a perpendicular line segment from a vertex to the line containing the opposite side.

For a triangle with an obtuse angle, the orthocenter lies outside of the triangle. This is because the altitudes from the acute angles of the triangle need to be extended beyond their adjacent sides in order to intersect, which means the point of intersection cannot lie within the triangle itself. Hence, when a triangle has an obtuse angle, we can assert with confidence that its orthocenter's position relative to the triangle is outside of it.

Therefore, the correct option is: B) Outside the triangle.