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MATH / A regular tetrahedron is a pyramid with four faces, each of which is an…

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problem

A regular tetrahedron is a pyramid with four faces, each of which is an equilateral triangle. Let ABCDABCD be a regular tetrahedron and let PP be the unique point equidistant from points A,B,C,DA,B,C,D. Extend AP→\overrightarrow{AP} to hit face BCDBCD at point QQ. What is the ratio PQ/AQPQ/AQ ?
Plain-text mathematical notation (without MathML)
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 (AP)→ to hit face BCD at point Q. What is the ratio PQ/AQ ?
Original LaTeX notation
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 $PQ/AQ$ ?

level

Level 5

type

Geometry

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Source and history

task_id
35a95712-e09f-5621-ac60-ab895653a178
task_key
geometry--test--35a95712-e09f-5621-ac60-ab895653a178
task_revision_id
1
config / split
geometry / test

Official source

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