1964 AHSME Problems/Problem 13
Problem 13
A circle is inscribed in a triangle with side lengths , and
. Let the segments of the side of length
,
made by a point of tangency, be
and
, with
. What is the ratio
?
Solution
Label our triangle where that
,
, and
. Let
,
, and
be the tangency points of
,
, and
respectively. Let
, which implies
. Thus
and
.
Since ,
. Thus
, hence our answer is
.