### Some(?) of the Parts

A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

### At a Glance

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

# Out of the Window

##### Stage: 4 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

I have four rectangular pieces of thin hardboard whose dimensions (in cm) are 55 x 85, 65 x 75, 65 x 85, 90 x 105. Without bending the hardboard, how many of these can I get through an open rectangular window measuring 60 cm x 80 cm?

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.