Inscribed circle

Calculate the magnitude of the BAC angle in the triangle ABC if you know that it is 3 times less than the angle BOC, where O is the center of the circle inscribed in the triangle ABC.

Correct result:

A =  36 °

Solution:

$$\begin{gathered} A+B+C=180 \\ A=O\mathrm{/}3 \\ C\mathrm{/}2+O+B\mathrm{/}2=180 \\ C\mathrm{/}2+P+A\mathrm{/}2=180 \\ B\mathrm{/}2+Q+A\mathrm{/}2=180 \\ B=rand(1{\dots }_{120}) \\ O=108^{\circ } \\ A=O\mathrm{/}3=108\mathrm{/}3=36^{\circ } \end{gathered}$$

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