### 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?

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

# Smartphone Screen

##### Age 14 to 16 ShortChallenge Level

A smartphone's display is given as the diagonal distance between the vertices. A certain smartphone has a 5 inch display and a resolution of 1920 pixels (length) x 1200 pixels (width).

What are the length and width of the display, in inches? Leave your answer in the form $\dfrac{a}{\sqrt b}$, where $a$, $b$ are integers.

This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.