Difference between revisions of "2020 AIME I Problems/Problem 15"
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/* Geogebra to Asymptote conversion, documentation at artofproblemsolving.com/Wiki go to User:Azjps/geogebra */ | /* Geogebra to Asymptote conversion, documentation at artofproblemsolving.com/Wiki go to User:Azjps/geogebra */ |
Revision as of 16:32, 12 March 2020
Note: Please do not post problems here until after the AIME.
Problem
Solution
The following is a power of a point solution to this menace of a problem:
Let points be what they appear as in the diagram below. Note that is not insignificant; from here, we set
by PoP and trivial construction. Now,
is the reflection of
over
. Note
, and therefore by Pythagorean theorem we have
. Consider
. We have that
, and therefore we are ready to PoP with respect to
. Setting
, we obtain
by PoP on
, and furthermore, we have
. Now, we get
, and from
we take
However, squaring and manipulating with
yields that
and from here, since
we get the area to be
. ~awang11's sol
See Also
2020 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Last Problem | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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