2021 JMPSC Invitationals Problems/Problem 10
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Problem
A point is chosen in isosceles trapezoid
with
,
,
, and
. If the sum of the areas of
and
is
, then the area of
can be written as
where
and
are relatively prime. Find
Solution
t is implied lies on the line that bisects
and
. We have the area of the trapezoid is
since the height is
. Now, subtracting
we have
for
is the height of
. This means
, asserting the area of
is
~Geometry285
See also
- Other 2021 JMPSC Invitationals Problems
- 2021 JMPSC Invitationals Answer Key
- All JMPSC Problems and Solutions
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