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Omni-MATH / A unit square ABCD and a circle Γ have the following property: if P is a point in the plane not contained in the interior of Γ, then min(∠APB,∠BPC,∠CPD,∠DPA)≤60^(∘). The minimum po…

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problem

A unit square ABCDA B C D and a circle Γ\Gamma have the following property: if PP is a point in the plane not contained in the interior of Γ\Gamma, then min(∠APB,∠BPC,∠CPD,∠DPA)≤60∘\min (\angle A P B, \angle B P C, \angle C P D, \angle D P A) \leq 60^{\circ}. The minimum possible area of Γ\Gamma can be expressed as aπb\frac{a \pi}{b} for relatively prime positive integers aa and bb. Compute 100a+b100 a+b.
Plain-text mathematical notation (without MathML)
A unit square ABCD and a circle Γ have the following property: if P is a point in the plane not contained in the interior of Γ, then min(∠APB,∠BPC,∠CPD,∠DPA)≤60^(∘). The minimum possible area of Γ can be expressed as (aπ)/(b) for relatively prime positive integers a and b. Compute 100a+b.
Original LaTeX notation
A unit square $A B C D$ and a circle $\Gamma$ have the following property: if $P$ is a point in the plane not contained in the interior of $\Gamma$, then $\min (\angle A P B, \angle B P C, \angle C P D, \angle D P A) \leq 60^{\circ}$. The minimum possible area of $\Gamma$ can be expressed as $\frac{a \pi}{b}$ for relatively prime positive integers $a$ and $b$. Compute $100 a+b$.

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task_id
3bc2b7e1-3a21-565b-958c-dc195137ec11
task_key
test--3bc2b7e1-3a21-565b-958c-dc195137ec11
task_revision_id
1
config / split
/ test

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