### Look Before You Leap

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?

### Triangle Midpoints

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

### Guillotine

Weekly Problem 9 - 2006
What fraction of the area of the rectangle is shaded?

# Points in Pairs

##### Stage: 4 Challenge Level:

What is the ratio $OP : OQ$ ?

Compare it with the ratio $OQ' : OP'$.