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Omni-MATH / Regular tetrahedron ABCD is projected onto a plane sending A,B,C, and D to A^{prime}, B^{prime}, C^{prime}, and D^{prime} respectively. Suppose …

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problem

Regular tetrahedron ABCDA B C D is projected onto a plane sending A,B,CA, B, C, and DD to $A^{\prime}, B^{\prime}, C^{\prime}$, and $D^{\prime}$ respectively. Suppose $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ is a convex quadrilateral with $A^{\prime} B^{\prime}=A^{\prime} D^{\prime}$ and $C^{\prime} B^{\prime}=C^{\prime} D^{\prime}$, and suppose that the area of $A^{\prime} B^{\prime} C^{\prime} D^{\prime}=4$. Given these conditions, the set of possible lengths of ABA B consists of all real numbers in the interval [a,b)[a, b). Compute bb.
Plain-text mathematical notation (without MathML)
Regular tetrahedron ABCD is projected onto a plane sending A,B,C, and D to $A^{\prime}, B^{\prime}, C^{\prime}$, and $D^{\prime}$ respectively. Suppose $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ is a convex quadrilateral with $A^{\prime} B^{\prime}=A^{\prime} D^{\prime}$ and $C^{\prime} B^{\prime}=C^{\prime} D^{\prime}$, and suppose that the area of $A^{\prime} B^{\prime} C^{\prime} D^{\prime}=4$. Given these conditions, the set of possible lengths of AB consists of all real numbers in the interval [a,b). Compute b.
Original LaTeX notation
Regular tetrahedron $A B C D$ is projected onto a plane sending $A, B, C$, and $D$ to $A^{\prime}, B^{\prime}, C^{\prime}$, and $D^{\prime}$ respectively. Suppose $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ is a convex quadrilateral with $A^{\prime} B^{\prime}=A^{\prime} D^{\prime}$ and $C^{\prime} B^{\prime}=C^{\prime} D^{\prime}$, and suppose that the area of $A^{\prime} B^{\prime} C^{\prime} D^{\prime}=4$. Given these conditions, the set of possible lengths of $A B$ consists of all real numbers in the interval $[a, b)$. Compute $b$.

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Source and history

task_id
9c8b73b3-9b29-53c4-b7f2-1fddb8cd451a
task_key
test--9c8b73b3-9b29-53c4-b7f2-1fddb8cd451a
task_revision_id
1
config / split
/ test

Official source

initial import