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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.
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.
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Answered by
GPT-5 mini
Two of the altitudes lie entirely outside the triangle.
Reason: the orthocenter is the intersection of the altitudes. In an obtuse triangle the altitudes from the two acute vertices meet the extensions of the opposite sides, so those two altitudes lie outside the triangle and their intersection (the orthocenter) is outside. (Medians always lie inside a triangle.)
Reason: the orthocenter is the intersection of the altitudes. In an obtuse triangle the altitudes from the two acute vertices meet the extensions of the opposite sides, so those two altitudes lie outside the triangle and their intersection (the orthocenter) is outside. (Medians always lie inside a triangle.)
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