Answer: Choice C. 107.9 degrees (approximate)
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Explanation:
Draw a line segment from A to B. Mark point E as the intersection between this new line segment and the arc CD.
We can see that AE = 4000 because it's another radius of the same circle. The diagram shows that EB = 2800.
So,
AB = AE+EB = 4000+2800 = 6800
Because point D is a tangent point, this means radius AD is perpendicular to tangent segment BD. We have a 90 degree angle at point D, or we can write angle BDA = 90.
With triangle BDA being a right triangle, we can use a trig ratio to compute angle DAB. I'll call this angle A for short.
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Apply the cosine ratio. Focus entirely on triangle BDA.
cos(angle) = adjacent/hypotenuse
cos(A) = AD/AB
cos(A) = 4000/6800
cos(A) = 10/17
A = arccos(10/17)
A = 53.9681209275294 ... make sure your calc is in degree mode
A = 53.968
Angle DAB = 53.968 degrees approximately
This represents exactly half of central angle CAD, so we'll double the value to get 2*53.968 = 107.936 which rounds to 107.9 degrees showing why choice C is the answer.
Central angle CAD is exactly equal to the arc it cuts off, minor arc CD. The central angle is roughly 107.9 degrees of a full 360 degree circle, and the same can be said about the outer arc edge piece of minor arc CD.
