AC is the tangent line, AB is the chord of the circle centered at point O, the angle AOB is 70 degrees

AC is the tangent line, AB is the chord of the circle centered at point O, the angle AOB is 70 degrees. What is the BAC angle.

In the AOB triangle, the sides OA and OB are equal as the radii of a circle, then the AOB triangle is isosceles, which means the angle OAB = OBA.

The sum of the inner angles of the triangle is 180, then the angle OAB = OBA = (180 – 75) / 2 = 52.5.

The angle OAC is 90, since the radius OA of the circle is drawn to the point of tangency of the tangent CA with the circle.

Then the angle BAC = 90 – ОАВ = 90 – 52.5 = 37.5.

Chord AB can be located in the opposite direction (indicated by a dotted line), then the angle BAC = 90 + 52.5 = 142.5.

Answer: The value of the angle BAC is 37.5 or 142.5.