1993 AIME Problems/Problem 15
Problem
Let be an altitude of
. Let
and
be the points where the circles inscribed in the triangles
and
are tangent to
. If
,
, and
, then
can be expressed as
, where
and
are relatively prime integers. Find
.
Solution
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From the Pythagorean Theorem, , and
. Subtracting those two equations yields
. After simplification, we see that
, or
. Note that
. Therefore we have that
. Therefore
.
Now note that ,
, and
. Therefore we have
.
Plugging in and simplifying, we have
.
See also
1993 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Last question | |
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