### 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

### Ladder and Cube

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?

# Interior Squares

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

The diagram shows a square of area x square units inscribed inside a semicircle and a larger square of area $y$ square units inscribed inside a circle.
What is the ratio $x : y$ ?

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.