2020 AIME I Problems/Problem 1
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Contents
Problem
Let be a parallelogram. Extend
through
to a point
and let
meet
at
and
at
Given that
and
find
Solution
Solution 1
There are several similar triangles. , so we can write the proportion:
Also, , so:
Substituting,
Thus, .
Solution 2
We have so
. We also have
so
. Equating the two results gives
and so
which solves to