Why do this
At first sight there might not seem to be enough information given
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
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
Can we make a list of everything that is known from the information
Can we see a way of using the information given to find the area of
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?