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Omni-MATH / Let ABCD be a tetrahedron such that its circumscribed sphere of radius R and its inscribed sphere of radius r are concentric. Given that AB=AC=1≤BC and R=4r, find BC².

Problem

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problem

Let ABCDA B C D be a tetrahedron such that its circumscribed sphere of radius RR and its inscribed sphere of radius rr are concentric. Given that AB=AC=1≤BCA B=A C=1 \leq B C and R=4rR=4 r, find BC2B C^{2}.
Plain-text mathematical notation (without MathML)
Let ABCD be a tetrahedron such that its circumscribed sphere of radius R and its inscribed sphere of radius r are concentric. Given that AB=AC=1≤BC and R=4r, find BC².
Original LaTeX notation
Let $A B C D$ be a tetrahedron such that its circumscribed sphere of radius $R$ and its inscribed sphere of radius $r$ are concentric. Given that $A B=A C=1 \leq B C$ and $R=4 r$, find $B C^{2}$.

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Source and history

task_id
00348d2c-0c54-5b19-9da9-25753f2ebaba
task_key
test--00348d2c-0c54-5b19-9da9-25753f2ebaba
task_revision_id
1
config / split
/ test

Official source

initial import