2023 SSMO Team Round Problems/Problem 3
Problem
Let be a triangle such that
and
Let
be the circumcircle of
. Let
be on the circle such that
Let
be the point diametrically opposite of
. Let
be the point diametrically opposite
. Find the area of the quadrilateral
in terms of a mixed number
. Find
.
Solution
Note that is right with the right angle at
. This means that
is the diameter of the circle. We can divide quadrilateral
into