Problem:
An isosceles trapezoid is circumscribed around a circle. The longer base of the trapezoid is , and one of the base angles is . Find the area of the trapezoid.
Answer Choices:
A.
B.
C.
D.
E. not uniquely determined
Solution:
By viewing the sides of the trapezoid as tangents to the circle, we find that the sums of the lengths of opposite sides are equal. (Indeed, this is true for any circumscribed quadrilateral.) Defining and as shown in the figure, we have
Then , and the area is .
