Difference between revisions of "2023 SSMO Speed Round Problems/Problem 8"
(Created page with "==Problem== ==Solution== Let <math>r</math> be the radius of <math>\omega</math> and let <math>C</math> be the midpoint of <math>AB</math> and let <math>OC = x.</math> Note...") |
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Revision as of 14:21, 3 July 2023
Problem
Solution
Let be the radius of and let be the midpoint of and let Note that . WLOG assume that
Since and we have
By the Pythagorean Theorem, we have which is the same as Solving for and we have that Thus, meaning that the minimum and maximum value of are both so the answer is