Prove that if the line through the centroid and the incenter is parallel to a side then the sides of the triangle form an arithmetic sequence.
Follow Math Help Forum on Facebook and Google+
Suppose that (I=incenter, G=centroid).
Let be the inradius, the height from the vertex A, the area of triangle and the semiperimeter.
Then we have
But and that means that b, a, c (or c, a, b) are in arithmetic progression.
View Tag Cloud