Q. The value of `alpha` for which the point `(alpha,alpha+2)` is an interior point of smaller segment of curve `x^2 + y^2 - 4=0` made by the chord of the curve whose equation is `3x + 4y + 12=0` .

A) `(-alpha, -20/7)`

B) `(-2,0)`

C) `(-alpha,20/7)`

D) `alpha` `in` `phi`

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To analyze the situation, first graph the shapes in question:

The curve with the equation `x^2 +y^2 - 4 =0` is a circle with the center in origin and radius 2, which can be seen by rewriting this equation in standard form:

`x^2+y^2 = 4 = 2^2`

The curve with the equation `3x+4y+12=0` is a line with intercepts (-4, 0) and (0, -3).

This is the graph of the above on the coordinate plane:

These curves do not intersect, so there is no smaller segment of the circle made by the chord of the line.

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