The chord AB subtracts a circular arc of 47 °. The tangents to the circle drawn at points A and B meet

The chord AB subtracts a circular arc of 47 °. The tangents to the circle drawn at points A and B meet at point O. Find the angle AOB.

Since the chord AB cuts off the arc 47, the central angle AO1B is also equal to 47.

By the property of the tangent drawn to the circle, the radius drawn to the point of tangency is perpendicular to the tangent. Then the angle O1BO and O1AO are straight lines.

Consider a quadrangle AOBO1, the sum of the internal angles of which is 360, then the angle AOB = 360 – O1BO – O1AO – AO1B = 360 – 90 – 90 – 47 = 133.

Answer: Angle AOB is 133.