Why do this
problem?
At first sight there might not seem to be
enough information given in this
question to find a solution. The first step is to interpret
what is known from the geometry given the inscribed circle, and
then to evaluate that information in terms of how it might be
used to express what is known in terms of the three variables
$a$, $b$ and $r$ and how that might be used to give an expression
for the area of the triangle.
One of the methods of solving this problem is an application of
the formula for tan$(A + B)$ combined with the formula for the
area of a triangle.
Possible
approach
Set this as an exercise in applying the
formula for $tan(A + B)$ or better still, if you want the
students to revise their trigonometry, you can make it a more
challenging problem solving activity and leave it to the students
to decide what they have to use.
Key questions
Can
we make a list of everything that is known from the information
given?
Can we see a way of using the information given to find the area
of the triangle?
Can we add lines to make pairs of congruent triangles?
Can we find the area of the whole triangle in terms of these
smaller congruent triangles?
What can we say about the angles at the centre of the
circle?
If three of the angles at the centre add up to $180$ degrees what
can we say about the tangents of these angles?