### 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.

# Semicircle Distance

##### Age 14 to 16 ShortChallenge Level

The diagram shows a rectangle and two semicircles.

The height of the rectangle 10 cm, and the area of the shaded region is 125 cm$^2$.

What is the shortest distance between the two semicircles?

Give your answer in terms of $\pi$.

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