### Look Before You Leap

Can you spot a cunning way to work out the missing length?

### 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:
See all short problems arranged by curriculum topic in the short problems collection

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.