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.

Answer 1

All three of the altitudes lie entirely outside the triangle.

Explanation:

We are asked to choose the best option that explains why the orthocenter of an obtuse triangle is outside the triangle.

We know that orthocenter of a triangle is the point where all three altitudes of the triangle intersect.

We also know that orthocenter of an obtuse triangle is always outside of the circle.

Since all three altitudes of an obtuse triangle intersect outside the triangle, therefore, orthocenter of an obtuse triangle is outside the triangle and option A is the correct choice.