A regular tetrahedron is a pyramid with four faces, each of which is an equilateral triangle.

Let $ABCD$ be a regular tetrahedron and let $P$ be the unique point equidistant from points $A,B,C,D$. Extend $\overrightarrow{AP}$ to hit face $BCD$ at point $Q$. What is the ratio $PQ/AQ$ ?
Question:
A regular tetrahedron is a pyramid with four faces, each of which is an equilateral triangle.

Let $ABCD$ be a regular tetrahedron and let $P$ be the unique point equidistant from points $A,B,C,D$. Extend $\overrightarrow{AP}$ to hit face $BCD$ at point $Q$. What is the ratio $PQ/AQ$ ?
Answer:
Let's think step by step.

user
\frac{1}{4}
A regular tetrahedron is a pyramid with four faces, each of which is an equilateral triangle.

Let $ABCD$ be a regular tetrahedron and let $P$ be the unique point equidistant from points $A,B,C,D$. Extend $\overrightarrow{AP}$ to hit face $BCD$ at point $Q$. What is the ratio $PQ/AQ$ ?
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