



 
Draw a diagram! P is the centre of the inscribed circle and r is its radius. Join P to each of the triangle vertices to partition the triangle ABC into three triangles. Look at one of these triangles PBC. D is the point on BC where the inscribed triangle touches the side. BC is tangent to the circle at this point so angle PDC is a right angle and hence r is the height of triangle PBC. What is the area of triangle PBC? In a similar way find the areas of triangles PCA and PAB. Their sum is the area of triangle ABC. Penny  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 