+977 In triangle $PQR$, let $M$ be the midpoint of $\overline{PQ}$, let $N$ be the midpoint of $\overline{PR}$, and let $O$ be the intersection of $\overline{QN}$ and $\overline{RM}$, as shown. If $\overline{QN}\perp\overline{PR}$, $QN = 1$, and $PR =1$, then find $OR$.
0 O is the centroid of the triangle and divides the medians in ratio 2:1. So:
ON+QO=QN=1ONQO=12ON=13
Also, N is the midpoint of PR so:
NR=PR2=12
Finally using pythagorean theorem on △ONR we get:
OR=√NR2+ON2OR=√132+122OR=√136
