Question 5
Let $ABCDE$ be a convex pentagon satisfying the following conditions:
* There is a circle $\Gamma$ tangent to each of its sides.
* The lengths of all its sides are integers.
* At least one side of the pentagon has length $1$.
* Side $AB$ has length $2$.
Let $P$ be the point of tangency of $\Gamma$ with side $AB$.
a) Determine the lengths of segments $AP$ and $BP$.
b) Give an example of a pentagon satisfying the stated conditions.
* There is a circle $\Gamma$ tangent to each of its sides.
* The lengths of all its sides are integers.
* At least one side of the pentagon has length $1$.
* Side $AB$ has length $2$.
Let $P$ be the point of tangency of $\Gamma$ with side $AB$.
a) Determine the lengths of segments $AP$ and $BP$.
b) Give an example of a pentagon satisfying the stated conditions.