An interesting question, so many ways to solve it. The question sheet (provided) includes scaffolding to help students solve the problem, however teachers are also encouraged to let students explore the problem. A simple geometric solution exists, but the problem is equally solvable using calculus. Students studying Specialist Mathematics also may like to use implicit differentiation, alternatively, some simple geometry can again be applied. So many ways to solve it.
One of the wonderful opportunities afforded by CAS is to allow students to explore more complex problems independently. In this delightful problem students can use Geometry, Calculus or a combination of the two, alternatively, the scaffolded version can be completed in around 15 to 20 minutes.
About the Lesson
The worksheet provides a series of scaffolded questions for students to follow and arrive at a solution. A teacher file however provides information on how else this activity can be used. The question can be solved using Geometry or Calculus or combinations thereof. The choice is yours, or theirs.