sum of 4 angles of 4 triangles with sideBC (2020 AESC MSU Internet Olympiad 7.5)

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sum of 4 angles of 4 triangles with sideBC (2020 AESC MSU Internet Olympiad 7.5)

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#1 h Feb 21, 2021, 10:28 AM

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On the plane there are four triangles with vertices at the vertices of cells with a common base $M N$ .
Find the sum of the angles of these triangles at the vertices $A, B, C, D$ .

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This post has been edited 1 time. Last edited by parmenides51, Feb 21, 2021, 10:29 AM

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#2 h Feb 21, 2021, 10:29 AM

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posted for the image link

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#3 h Feb 21, 2021, 11:55 AM

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Does this work?

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#4 h Feb 21, 2021, 5:50 PM

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$\tan^{-1} \frac{1}{4}+\tan^{-1}\frac{2}{3}-\tan^{-1}\frac{1}{3}+\tan^{-1}\frac{3}{2}-\tan^{-1} 1+\tan^{-1} 4-\tan^{-1} 3$ $\tan^{-1} \frac{14}{5}+\tan^{-1} \frac{3}{11}+\tan^{-1}\frac{1}{13}-\tan^{-1} 1$ $\tan^{-1} 13+\tan^{-1}\frac{1}{13}-\tan^{-1} 1$ $\frac{\pi}{2}-\frac{\pi}{4}$ $\frac{\pi}{4}$

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