Visual Representation of 2012 SMO Junior Question 6

Lew W. S.
Singapore Math Olympiad 2012 Junior Question 6 Use the slider to change values of x and explore visually the solution of Q6
1. What happens when you change the value of x ? Does the small circle increase in size ? Does the square increase in size? Can you write down the algebraic expression for the length of the side of the square? 2. What is the value of x when the square is as large as possible without extending out of the larger circle? 3. What is the value of x when the smaller circles touch each other? 4. Can you write down the algebra equation to sum up the lengths and diameters of the circles for part 2 & 3 question above?