2008 AMC 10B Problems/Problem 10

Revision as of 17:38, 10 August 2008 by BOGTRO (talk | contribs) (Problem)

Problem

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?

Solution

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.

See also

2008 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 9
Followed by
Problem 11
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All AMC 10 Problems and Solutions
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