MathDB

11

Part of 2005 AIME Problems

Problems(2)

A Semicircle and a Square

Source:

11/12/2005
A semicircle with diameter dd is contained in a square whose sides have length 88. Given the maximum value of dd is m−nm- \sqrt{n}, find m+nm+n.
geometryrotationrectanglesimilar triangles
A Sequence of Real Numbers

Source:

11/13/2005
Let mm be a positive integer, and let a0,a1,…,ama_0, a_1,\ldots,a_m be a sequence of reals such that a0=37a_0=37, a1=72a_1=72, am=0a_m=0, and ak+1=ak−1−3aka_{k+1}=a_{k-1}-\frac{3}{a_k} for k=1,2,…,m−1k=1,2, \dots, m-1. Find mm.
inductionSequences