Here, AB is tangent to the inside circle and we can rotate AB around the inside circle. In this model, the endpoint, D', of In this model, the endpoint the chord CD' can be moved along the circumference of the circle from the fixed point C. Since any angle inscribed in a semicircle is a right angle, we have that ACD is a right triangle. With these three interpretation, students can obtain three different solutions. Of course, a teacher should be able to understand the meaning of the problem and its solution process in each model. This problem is nicely made.
Students can use their knowledge from high school geometry in solving the problem.
The diameter of the circle is 2 and the length of the chord is , and the numbers and the theorems that are used in each model are familiar to the students. They learned all knowledge from their geometry class. Mathematics is not just a subject that requires a formula for a problem any more. The students obtain the three right answers so they can see that mathematics does not require a right answer all the time. Most of all, this problem is totally different from the other problems that students have encountered so far.