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?

Trapezium Four

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

Two Right Angles

Stage: 4 Short Challenge Level:

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.
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