2008 AMC 10B Problems/Problem 10

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?

Let the center of the circle be O. Draw lines

OA, OB, and OC.

OA=OB=5, since they are both radii.

OC bisects AB, and AB=6, so letting point D be

the intersection of AB and OC, AD=BD=3.

Also, OD=4. This means that CD=1.

Using the pythagorean theorem,

$AC=\sqrt{3^2+1^2}=\sqrt{10}$ .

Answer A is the correct answer.

2008 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 9	Followed by Problem 11
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