2017 AMC 12A Problems/Problem 24
Problem
Quadrilateral is inscribed in circle and has side lengths , and . Let and be points on
such that and . Let be the intersection of line and the line through parallel to . Let be the intersection of line and the line through parallel to . Let be the point on circle other than that lies on line . What is ?
Solution
It is easy to see that First we note that with a ratio of Then with a ratio of , so Now we find the length of . Because the quadrilateral is cyclic, we can simply use the Law of Cosines. By Power of a Point, . Thus
-solution by FRaelya
See Also
2017 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 23 |
Followed by Problem 25 |
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All AMC 12 Problems and Solutions |
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