The circle with center O touches the sides of the corner with vertex A at points B and C. Find the angle BAC

The circle with center O touches the sides of the corner with vertex A at points B and C. Find the angle BAC if the angle BOC is 114 degrees

If the sides of the corner touch the circle at points B and C, then OB and OC are perpendicular to the sides of the angle AB and AC, because the radius drawn to the tangent point is perpendicular to the tangent.

The sum of the angles of a quadrilateral is 360 °, so in quadrilateral ABOC the sum of the angles is 360 °.

Angles ABO and ACO are 90 ° each (as perpendiculars).

The BOC is 114 °.

Hence the angle BAC = 360 ° – (90 ° + 90 ° + 114 °) = 360 ° – 294 ° = 66 °.