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

Weekly Problem 4 - 2008

Triangles $QPR$ and $RPS$ are similar. So:$\frac{PR}{PS}=\frac{PQ}{PR}$. Hence $PR^2=PQ\times PS=\frac{7}{3}\times\frac{48}{7}=16$.

So $PR$ is $4$ units long.

This problem is taken from the UKMT Mathematical Challenges.