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Omni-MATH / Let H be a regular hexagon with side length one. Peter picks a point P uniformly and at random within H, then draws the largest circle with center P that is contained in H. What is…

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problem

Let H\mathcal{H} be a regular hexagon with side length one. Peter picks a point PP uniformly and at random within H\mathcal{H}, then draws the largest circle with center PP that is contained in H\mathcal{H}. What is this probability that the radius of this circle is less than 12\frac{1}{2}?
Plain-text mathematical notation (without MathML)
Let H be a regular hexagon with side length one. Peter picks a point P uniformly and at random within H, then draws the largest circle with center P that is contained in H. What is this probability that the radius of this circle is less than (1)/(2)?
Original LaTeX notation
Let $\mathcal{H}$ be a regular hexagon with side length one. Peter picks a point $P$ uniformly and at random within $\mathcal{H}$, then draws the largest circle with center $P$ that is contained in $\mathcal{H}$. What is this probability that the radius of this circle is less than $\frac{1}{2}$?

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Source and history

task_id
c53301ee-a0d4-5e5d-81be-af43620e0059
task_key
test--c53301ee-a0d4-5e5d-81be-af43620e0059
task_revision_id
1
config / split
/ test

Official source

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