# An interesting problem in Geometry

• Jun 8th 2010, 11:12 PM
simplependulum
An interesting problem in Geometry
In $\Delta ABC$ , a line passing through the centroid of the triangle intersects with segments $AB$ and $AC$ at $P$ and $Q$ respectively .

Show that :

$\frac{BP}{AP} + \frac{ CQ}{AQ} = 1$
• Jul 18th 2010, 09:38 PM
Sudharaka
Quote:

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

Show that :

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

Dear simplependulum,

Thanks for submitting this question. I tried it for several days and finally came up with an answer.
• Jul 18th 2010, 09:58 PM
simplependulum
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 !