Series of CirclesPro Problems > Math
Series of Circles
Triangle ABC is placed on a complex plane so that the modulus of A is 0, B = 12 + 0i and C can be represented in the form C = k + i
81 - k2, for some value of k. The area of the triangle is
Circle C1 lies in the first quadrant, and it is tangent to line AB and line AC. The radius of C1 is 1.
For each circle Cn (n > 1), circle Cn is also tangent to lines AB and AC, is externally tangent to circle Cn - 1, and its center is closer to point A than the center of circle Cn - 1.
Ellipse E has a major axis of length 4, and its area is equal to the sum of the areas of C1, C2, C3, ...
Find the eccentricity of ellipse E to the nearest 100th of a unit.
Note: This problem was designed for my honors students who have studied trigonometry, complex numbers, coordinate geometry and conics, and sequences and series this year. This problem incorporates elements of all of those areas of study.
Problem by Mr. Twitchell
SolutionIn order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.
Assign this problemClick here to assign this problem to your students.
Blogs on This Site
Reviews and book lists - books we love!
The site administrator fields questions from visitors.
Like us on Facebook to get updates about new resources