rumbleroar
Survivor of the HSC
- Joined
- Nov 30, 2011
- Messages
- 2,271
- Gender
- Female
- HSC
- 2014
Re: HSC 2014 4U Marathon
However, I think one person tried doing that and got marked down, because the question specifically stated hence and that meant they needed to use the previous parts.
Nice!!R is the centroid of triangle OPQ. By symmetry, triangle PQS is a reflection of triangle OPQ. Consider R' is the centroid of triangle PQS. A property of all triangles is the centroid divides the median (i.e. OM, QN, MS, etc) into the ratio 2:1. Thus OR:RM is 2:1 and similarly SR':MR' is 2:1.
Thus since OM=MS, then it follows that SR:OR is 2:1, hence
However, I think one person tried doing that and got marked down, because the question specifically stated hence and that meant they needed to use the previous parts.