The diagonals of a square meet at O. The bisector of angle OAB meets BO and BC at N and P respectively. The length of NO is 24. How long is PC?
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
weekly problem 9-2006
In the figure above, $PQ=2\frac{1}{3}$, $PS = 6\frac{6}{7}$, $PQR$ and $PRS$ are right-angled triangles, and the angles $QPR$ and $RPS$ are the same. How long is $PR$?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.