Do you know that the length of the arc of a circle that an angle subtends is proportional to the measure of the angle times the radius? In fact, radian measure isdefinedto be that arc length divided by the radius. The arc length is the measure of the angle, in radians, multiplied by the radius. The arclength is the measure of the angle, in degrees, multiplied by the radius also multiplied by [tex]\frac{\pi}{180}[/itex]. But in either case, the arclength is proportional to angle times the radius. And that means that the angle is proportional to arclengthdividedby the radius. As long as the arclength is constant, the angle is inversely proportional to the radius.

Here, both angles subtend the same arc (from B to C). But the "radius" for one angle is the radius of the circle while for the other it is the diameter.