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Omni-MATH / Find the smallest positive real constant a, such that for any three points A,B,C on the unit circle, there exists an equilateral triangle PQR with side length a such that all of …

Problem

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problem

Find the smallest positive real constant

a

, such that for any three points

A,B,C

on the unit circle, there exists an equilateral triangle

PQR

with side length

a

such that all of

A,B,C

lie on the interior or boundary of

\triangle PQR

Plain-text mathematical notation (without MathML)

Find the smallest positive real constant a, such that for any three points A,B,C on the unit circle, there exists an equilateral triangle PQR with side length a such that all of A,B,C lie on the interior or boundary of △PQR.

Original LaTeX notation

Find the smallest positive real constant $a$, such that for any three points $A,B,C$ on the unit circle, there exists an equilateral triangle $PQR$ with side length $a$ such that all of $A,B,C$ lie on the interior or boundary of $\triangle PQR$.

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task_id: 08a7a350-fb9e-5931-9719-b8ea47675c34
task_key: test--08a7a350-fb9e-5931-9719-b8ea47675c34
task_revision_id: 2
config / split: / test

Official source

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