# May 2002, Stage 4&5

## Problems

### Similarly So

##### Stage: 4 Challenge Level:

ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.

### Approximating Pi

##### Stage: 4 and 5 Challenge Level:

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?

### Double Angle Triples

##### Stage: 5 Challenge Level:

Try out this geometry problem involving trigonometry and number theory

### 30-60-90 Polypuzzle

##### Stage: 5 Challenge Level:

Re-arrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.

### Remainder Hunt

##### Stage: 5 Challenge Level:

What are the possible remainders when the 100-th power of an integer is divided by 125?

### Binary Squares

##### Stage: 5 Challenge Level:

If a number N is expressed in binary by using only 'ones,' what can you say about its square (in binary)?