# 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:

$A+B+C=180 \ \\ A=O/3 \ \\ C/2+O+B/2=180 \ \\ C/2+P+A/2=180 \ \\ B/2+Q+A/2=180 \ \\ B=rand(1...120) \ \\ \ \\ O=108 \ ^\circ \ \\ A=O/3=108/3=36 ^\circ$

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