2008 AMC 10B Problems/Problem 10
Problem
Points and are on a circle of radius and . Point is the midpoint of the minor arc . What is the length of the line segment ?
Solution
Let the center of the circle be , and let be the intersection of and (then is the midpoint of ). , since they are both radii.
By the Pythagorean Theorem, , and by subtraction, .
Using the Pythagorean Theorem again, .
See also
2008 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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All AMC 10 Problems and Solutions |