In a circle with center O, AB is a chord. A line segment CD is tangent to the circle at point A. If the angle CAD (the angle formed between the tangent CD and the chord AB) is 70 degree, what is the measure of the angle AOB (the angle subtended by the chord AB at the center of the circle)?

By the alternate segment theorem, the angle between the tangent CD and chord AB (angle CAD = 70) is equal to the angle subtended by the chord in the alternate segment. Thus, the angle at the circumference is 70 degrees. The angle subtended at the center (AOB) is twice the angle at the circumference, so 2 * 70 = 140 degrees.