So Big

One side of a triangle is divided into segments of length a and b by the inscribed circle, with radius r. Prove that the area is: abr(a+b)/ab-r^2

30-60-90 Polypuzzle

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

Bend

What is the longest stick that can be carried horizontally along a narrow corridor and around a right-angled bend?

Gold Again

Stage: 5 Challenge Level:
Find all the angles and lengths in the diagram. Use the cosine rule.