2018 AIME I Problems/Problem 2
Problem
What is the area of the polygon whose vertices are the points of intersection of the curves and
Solution
The first curve is a circle with radius centered at the origin, and the second curve is an ellipse with center
and end points of
and
. Finding points of intersection, we get
,
, and
, forming a triangle with height of
and base of
So the area of this triangle is $9 \cdot 6 \cdot 0.5 =27 $