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Question Number 180273 by Shrinava last updated on 09/Nov/22

$$\mathrm{In}\mathrm{triangle}\mathrm{ABC}\mathrm{with}\mathrm{angles}\alpha ,\beta ,\gamma$$$$\mathrm{correspondently},{\mathrm{Euler}}^{\prime }\mathrm{s}\mathrm{line}\mathrm{interescts}$$$$\mathrm{BC}\mathrm{at}\mathrm{point}\mathrm{P}.{\mathrm{Ite}}^{\prime }\mathrm{s}\mathrm{put}\delta \mathrm{is}\mathrm{angle}$$$$\mathrm{between}{\mathrm{Euler}}^{\prime }\mathrm{s}\mathrm{line}\mathrm{and}\mathrm{BC}\left(\mathrm{\angle }\mathrm{BPH}\right).$$$$\mathrm{Then}\mathrm{the}\mathrm{following}\mathrm{is}\mathrm{true}$$$$\tan \delta =\frac{2\cos \beta \cos \gamma -\cos \alpha }{\sin (\beta -\gamma )}$$

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