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Review: Circle, Triangle, and Arc
Explanation
We have both a circle and what appears to be a 45-45-90
triangle here, two geometric entities that tend to create situations of data
sufficiency. On to the statements, separately first.
Statement (1) tells us the area of the triangle. Each of
the non-hypotenuse sides is a radius of the circle so
and
, so we can find the area of the circle. Sufficient.
Statement (2) tells us the length of the arc ACB, which
includes the three-quarters of angle measure not encompasses by the right angle
of the triangle. Likewise, this arc will comprise three-quarters of the
circle's circumference, so we can write
. Again, we can find
, so we can determine the area of the circle.
Sufficient.
The correct answer is (D).
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