Question

Angle BCD is a circumscribed angle of circle A. Fast



What is the measure of angle BCD?

37°
53°
74°
106°

Answer 1

The image shown below goes with this question. 
Here, Angle BAC = 53.
In triangle ABC, the sum of the angles should be equal to 180 degrees according to the properties of a triangle. But, Angle CBA should be 90 because CB is a tangent to the circle. 
Hence, 
Angle BAC + Angle BCA + Angle ABC = 180 degrees
53 + Angle BCA + 90 = 180
Angle BCA + 143 = 180
Angle BCA = 180-143 = 37

Angle BCD = 2 x Angle BCA
                   = 2 x 37 = 74 degrees

Thus, Angle BCD is 74 degrees, Option c