2021 JMPSC Sprint Problems/Problem 18
Problem
On square with side length
,
is the midpoint of
. Let
be the foot of the altitude from
to
. If
can be represented as
for some integer
find the value of
Solution
Notice that since and
,
is a 45-45-90 triangle. Thus,
Also, we have
, so
which gives the answer of
.
~tigerzhang
See also
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