Difference between revisions of "2008 AMC 10B Problems/Problem 10"

Revision as of 16:38, 10 August 2008

Points A and B are on a circle of radius 5 and AB=6. Point C is the midpoint of the minor arc AB. What is the length of the line segment AC?

We know that $u_6=128$ , so we plug in $n=4$ to get $128=2u_5+u_4$ . We plug in $n=3$ to get

$u_5=2u_4+9$ . Substituting gives

$128=5u_4+18 \rightarrow u_4=22$

This gives $u_5=\frac{128-22}{2}=53$ .

Answer B is the correct answer

NOTE: This is my (BOGTRO) solution, not the official one,

and should be ignored in view of a better solution.

2008 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 9	Followed by Problem 11
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 10 Problems and Solutions

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 ==Problem==
-Suppose that <math>(u_n)</math> is a serquence of real numbers satifying <math>u_{n+2}=2u_{n+1}+u_n</math>,
+Points A and B are on a circle of radius 5 and AB=6. Point C is the midpoint of the minor arc AB. What is the length of the line segment AC?
-and that <math>u_3=9</math> and <math>u_6=128</math>. What is <math>u_5</math>?
-(A) 40 (B) 53 (C) 68 (D) 88 (E) 104
 ==Solution==