Please help me find arc CD

Choice C.  107.9 degrees   (approximate)

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.

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.

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step-by-step explanation:

a

b

d

step-by-step explanation: