2021 JMPSC Invitationals Problems/Problem 10
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
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, edited by CyclicISLscelesTrapezoid
See also
- Other 2021 JMPSC Invitationals Problems
- 2021 JMPSC Invitationals Answer Key
- All JMPSC Problems and Solutions
The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition.