# Thread: An interesting problem in Geometry

1. ## An interesting problem in Geometry

In $\displaystyle \Delta ABC$ , a line passing through the centroid of the triangle intersects with segments $\displaystyle AB$ and $\displaystyle AC$ at $\displaystyle P$ and $\displaystyle Q$ respectively .

Show that :

$\displaystyle \frac{BP}{AP} + \frac{ CQ}{AQ} = 1$

2. Originally Posted by simplependulum
In $\displaystyle \Delta ABC$ , a line passing through the centroid of the triangle intersects with segments $\displaystyle AB$ and $\displaystyle AC$ at $\displaystyle P$ and $\displaystyle Q$ respectively .

Show that :

$\displaystyle \frac{BP}{AP} + \frac{ CQ}{AQ} = 1$
Dear simplependulum,

Thanks for submitting this question. I tried it for several days and finally came up with an answer.

3. Thanks for the reply , I worried that no one may feel interested in this problem which seems an easy task but actually it needs some time to finish .

Excellent ! You utilized Menelaus Theorem to solve this problem . I think Menelaus and Ceva is one of the greatest stone in pure geometry , they are applicable and powerful indeed !