MathDB

1

Part of 1994 India National Olympiad

Problems(1)

Prove another similarity!

Source: INMO 1994 Problem 1

10/6/2005
Let GG be the centroid of the triangle ABCABC in which the angle at CC is obtuse and ADAD and CFCF be the medians from AA and CC respectively onto the sides BCBC and ABAB. If the points  B, D, G\ B,\ D, \ G and  F\ F are concyclic, show that ACBC≥2\dfrac{AC}{BC} \geq \sqrt{2}. If further PP is a point on the line BGBG extended such that AGCPAGCP is a parallelogram, show that triangle ABCABC and GAPGAP are similar.
geometryparallelogramratiogeometry solved