### Degree Ceremony

What does Pythagoras' Theorem tell you about these angles: 90Â°, (45+x)Â° and (45-x)Â° in a triangle?

### Logosquares

Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.

### Ball Bearings

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

# Geometric Trig

##### Age 16 to 18 ShortChallenge Level

This problem uses basic notions of trigonometry and areas of triangles which are fundamental to developments in A-level mathematics.

Being able to work with diagrams such as this is useful prepation for both coordinate geometry and mechanics.