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Omni-MATH / Let ∠XOY=(π)/(2); P is a point inside ∠XOY and we have OP=1;∠XOP=(π)/(6). A line passes P intersects the Rays OX and OY at M and N. Find the maximum value of OM+ON−MN.

Problem

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problem

Let ∠XOY=π2\angle XOY = \frac{\pi}{2}; PP is a point inside ∠XOY\angle XOY and we have OP=1;∠XOP=π6.OP = 1; \angle XOP = \frac{\pi}{6}. A line passes PP intersects the Rays OXOX and OYOY at MM and NN. Find the maximum value of OM+ON−MN.OM + ON - MN.
Plain-text mathematical notation (without MathML)
Let ∠XOY=(π)/(2); P is a point inside ∠XOY and we have OP=1;∠XOP=(π)/(6). A line passes P intersects the Rays OX and OY at M and N. Find the maximum value of OM+ON−MN.
Original LaTeX notation
Let $\angle XOY = \frac{\pi}{2}$; $P$ is a point inside $\angle XOY$ and we have $OP = 1; \angle XOP = \frac{\pi}{6}.$ A line passes $P$ intersects the Rays $OX$ and $OY$ at $M$ and $N$. Find the maximum value of $OM + ON - MN.$

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Source and history

task_id
057c537c-be0e-5414-a65d-d7191e9e7e49
task_key
test--057c537c-be0e-5414-a65d-d7191e9e7e49
task_revision_id
5
config / split
/ test

Official source

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