Some Considerations About A Triangular Pyramid

Geometry Level 4

A pyramid with vertex $V$ has a triangular base $\triangle ABC$ . The three lateral edges $VA$ , $VB$ and $VC$ are congruent. Let $H$ be the orthogonal projection of the point $V$ on $\triangle ABC$ .

Which of these affirmations is true about point $H$ ?

It can coincide with one of the points

A

B

C

It coincides with the orthocenter of

\triangle ABC

It always lies inside

\triangle ABC

It coincides with the circumcenter of

\triangle ABC

It always lies outside

\triangle ABC

1 solution

Michael Mendrin
Jun 28, 2016

Use Pythagorean's Theorem, given altitude of pyramid, H is equidistant from points A, B, C.

Some Considerations About A Triangular Pyramid

1 solution

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