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

A 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 = 127 degrees.

By the property of the tangent to the circle, the radius of the circle drawn to the tangent point forms an angle of 90 with the tangent.

Consider a quadrangle ABOС, which, by condition, has an angle BOС = 1270, and by construction, the angle OBA = OCA = 90.

Since the sum of the angles of a convex quadrilateral is 360, the angle BАС = 360 – BОС – ОВА – OCA = 360 – 127 – 90 – 90 = 53.

Answer: The BAC angle is 53.