Skip over navigation
Interior Squares
Age 14 to 16
ShortChallenge Level 
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.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
You may also like
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?