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Omni-MATH / Let ABC be an equilateral triangle with AB=3. Circle ω with diameter 1 is drawn inside the triangle such that it is tangent to sides AB and AC. Let P be a point on ω and Q be a poi…

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problem

Let ABCA B C be an equilateral triangle with AB=3A B=3. Circle ω\omega with diameter 1 is drawn inside the triangle such that it is tangent to sides ABA B and ACA C. Let PP be a point on ω\omega and QQ be a point on segment BCB C. Find the minimum possible length of the segment PQP Q.
Plain-text mathematical notation (without MathML)
Let ABC be an equilateral triangle with AB=3. Circle ω with diameter 1 is drawn inside the triangle such that it is tangent to sides AB and AC. Let P be a point on ω and Q be a point on segment BC. Find the minimum possible length of the segment PQ.
Original LaTeX notation
Let $A B C$ be an equilateral triangle with $A B=3$. Circle $\omega$ with diameter 1 is drawn inside the triangle such that it is tangent to sides $A B$ and $A C$. Let $P$ be a point on $\omega$ and $Q$ be a point on segment $B C$. Find the minimum possible length of the segment $P Q$.

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Source and history

task_id
047eaa93-18fd-51a5-aab5-52df84de3605
task_key
test--047eaa93-18fd-51a5-aab5-52df84de3605
task_revision_id
1
config / split
/ test

Official source

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