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AMC 12 B #0kj9

AMC 12 BHard

From module Angle Chasing Mastery

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Understand the scale
Scale 0.5: Easiest math competition problems, often solvable even for early middle school students without experience. 1: Problems strictly for beginners, often at a moderate middle school level. 1.5: Problems for stronger beginner students, on the level of the middling problems in most middle school contests. 2: For motivated beginners, harder questions from the previous categories. 2.5: More advanced beginner problems, hardest questions from previous categories. 3: Early intermediate problems that require more creative thinking. 3.5: Tougher early intermediate problems that consistently stretch into higher-level creative thinking or conceptual knowledge. 4: Intermediate-level problems. 4.5: Upper intermediate problems approaching the upper bound for non-invitational sprint math competitions. 5: More difficult AIME problems or simple proof-based Olympiad-style problems. 6: High-level AIME-styled questions or introductory Olympiad-level questions. 7: Tougher Olympiad-level questions, may require more technical knowledge. 8: High-level Olympiad-level questions. 9: Expert Olympiad-level questions. 9.5: The hardest problems appearing on Olympiads which the strongest students could reasonably solve. 10: Historically notorious problems, generally unsuitable for even very hard competitions because they are exceedingly tedious, long, and difficult.
TangentsCartesian coordinatesAngle chasing

Problem

Right triangle ABCABC has side lengths BC=6BC = 6, AC=8AC = 8, and AB=10AB = 10. A circle centered at OO is tangent to line BCBC at BB and passes through AA. A circle centered at PP is tangent to line ACAC at AA and passes through BB. What is OPOP? (A) 238\frac{23}{8} (B) 2910\frac{29}{10} (C) 3512\frac{35}{12} (D) 7325\frac{73}{25} (E) 3

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