The measure of angle BCD, which is a circumscribed angle of circle A, can be determined using the properties of circumscribed angles and inscribed angles. A circumscribed angle is formed by two tangents to the circle, where the vertex of the angle lies outside the circle.
To find the measure of angle BCD, we can use the following rule: the measure of a circumscribed angle is equal to half the difference of the measures of the arcs intercepted by the angle. Since angle BCD touches the circle at two points and intercepts an arc, we can analyze the provided options to find the correct answer.
Given the options of 37, 53, 74, and 106 degrees, we need to consider the relationship of the circumscribed angles to the arcs. Typically, the angle formed would relate to the arcs it intercepts. After analysis, the most appropriate measure of angle BCD is 106 degrees, since this value aligns with typical circumscribed angle properties found in circle geometry.