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Omni-MATH / Let a≠b be positive real numbers and m,n be positive integers. An m+n-gon P has the property that m sides have length a and n sides have length b. Further suppose that P can be ins…

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problem

Let a≠ba \neq b be positive real numbers and m,nm, n be positive integers. An m+nm+n-gon PP has the property that mm sides have length aa and nn sides have length bb. Further suppose that PP can be inscribed in a circle of radius a+ba+b. Compute the number of ordered pairs (m,n)(m, n), with m,n≤100m, n \leq 100, for which such a polygon PP exists for some distinct values of aa and bb.
Plain-text mathematical notation (without MathML)
Let a≠b be positive real numbers and m,n be positive integers. An m+n-gon P has the property that m sides have length a and n sides have length b. Further suppose that P can be inscribed in a circle of radius a+b. Compute the number of ordered pairs (m,n), with m,n≤100, for which such a polygon P exists for some distinct values of a and b.
Original LaTeX notation
Let $a \neq b$ be positive real numbers and $m, n$ be positive integers. An $m+n$-gon $P$ has the property that $m$ sides have length $a$ and $n$ sides have length $b$. Further suppose that $P$ can be inscribed in a circle of radius $a+b$. Compute the number of ordered pairs $(m, n)$, with $m, n \leq 100$, for which such a polygon $P$ exists for some distinct values of $a$ and $b$.

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Source and history

task_id
d9b515af-d87e-561f-a20e-852cf9945b81
task_key
test--d9b515af-d87e-561f-a20e-852cf9945b81
task_revision_id
1
config / split
/ test

Official source

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