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AMC 10 A #0khq

AMC 10 AHard

From module Cyclic Quadrilaterals

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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.
TangentsCyclic quadrilateralsTriangle centers: centroid, incenter, circumcenter, orthocenter, Euler line, nine-point circleAngle chasingDistance chasing

Problem

Isosceles triangle ABCABC has AB=AC=36AB = AC = 3\sqrt{6}, and a circle with radius 525\sqrt{2} is tangent to line ABAB at BB and to line ACAC at CC. What is the area of the circle that passes through vertices AA, BB, and CC? (A) 24π24\pi (B) 25π25\pi (C) 26π26\pi (D) 27π27\pi (E) 28π28\pi

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