Difference between revisions of "2022 SSMO Speed Round Problems/Problem 10"
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Revision as of 14:04, 3 July 2023
Problem
In a circle centered at with radius we have non-intersecting chords and is outisde of quadrilateral and Let and Suppose that . If and , then for and squareless Find
Solution
Let .
Then, by power of the point we have that and subtracting gives that . Since we know that , dividing gives that so and .
Then, by law of cosines, it follows that which implies that .
Then, which implies that so the answer is then .