Pythagorean Circles Activity - Explanation
The purpose of this activity was to have the students take the smaller steps necessary to solve a problem which may, at first, seem too difficult. The original problem posed was as follows:
The diagonals of the rectangle OABC intersect at a point P. The point P lies on circle 1, O is the center of circles 1, 2 and 3, and AO = 3.
- Find the area of the annulus between circle 1 and circle 2.
- Find the area of the annulus between circle 2 and circle 3.
By breaking the activity into smaller parts, it allowed the students to work at their own pace, giving hints to the students that were having trouble. We also found that by doing the activity over two days of class the students were more involved the second time, possibly more invested by having already put time into their work.
In parts II.A and II.B we left blanks for the area and the radius of a circle. These parts were explained before they began that section.