Pentagon with integer sides & inscribed circle
Source: XVIII Cono Sur Mathematical Olympiad (2007)
August 10, 2011
geometry unsolvedgeometry
Problem Statement
Let be a convex pentagon that satisfies all of the following:
[*]There is a circle tangent to each of the sides.
[*]The lengths of the sides are all positive integers.
[*]At least one of the sides of the pentagon has length .
[*]The side has length .
Let be the point of tangency of with .
(a) Determine the lengths of the segments and .
(b) Give an example of a pentagon satisfying the given conditions.