How many of the three heights of triangle ABC do not pass inside the

Question

How many of the three heights of triangle ABC do not pass inside the triangle?

(1) ΔABC is obtuse.

(2) The altitude of A from BC does not pass inside ΔABC.

Kurtosis · Answer

St1: ABC is obtuse --> Suppose B is the obtuse angle and BC is the base. Project BC to a point D such that D is vertically below A then AD will be the height and will lie outside the triangle. Thus, there is one height that does not pass inside the triangle.

St2: The altitude of A from BC does not pass inside ΔABC. --> Sufficient.

Answer: D

St2: The altitude of A from BC does not pass inside ΔABC. --> Sufficient.

Answer: D

SOUMYAJIT_ · Answer

I did not understand this question. Diagrams please?

ar500 · Answer

It seems like there may be some language translation issues in this problem. What are heights and altitudes in the context of triangles? Are these supposed to be lengths and angles?

Bunuel · Answer

Height and altitude are the same thing - the altitude of a triangle is the perpendicular from the base to the opposite vertex. Check more here: https://gmatclub.com/forum/math-triangles-87197.html

Kurtosis · Answer

Attached figure for your reference. Notice that height AD lies outside the obtuse angled triangle ABC.

How many of the three heights of triangle ABC do not pass inside the

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