**In the following figure, an isosceles triangle**

*ABC*is perfectly enclosed in a semi-circle of radius*r*. If*AB*is a diameter of the semi-circle, which of the following expressions shows the combined area of the shaded regions in terms of*r*?
A.

*r*^{2}(π – 1) / 2
B

*. r*^{2}(π – 2)
C.

*r*^{2}(π – 2) / 2
D.

*r*^{2}(π – 1)*AB*= 2

*r*, and this segment must pass through the center of the circle. This means that the height of the triangle (to the vertex

*C*) must be equal to the radius

*r*. Thus the area of the triangle is 2

*r*(

*r*)/2 =

*r*

^{2}. Area of the semi-circle is π

*r*

^{2}/2. Thus the combined area of the shaded regions is π

*r*

^{2}/2 –

*r*

^{2}=

*r*

^{2}(π – 2) / 2. The correct answer choice is (C).

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