### At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

### Darts and Kites

Explore the geometry of these dart and kite shapes!

### No Right Angle Here

Prove that the internal angle bisectors of a triangle will never be perpendicular to each other.

# Angle to Chord

##### Age 14 to 16 ShortChallenge Level

$P$, $Q$ and $R$ are points on the circumference of a circle of radius 4cm. $\angle PQR=45^o$. What is the length of chord $PR$?

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.
You can find more short problems, arranged by curriculum topic, in our short problems collection.