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The Number of Points

Source: 1994 National High School Mathematics League, Exam One, Problem 9

March 2, 2020

Problem Statement

Point Sets A={(x,y)∣(x−3)2+(y−4)2≤(52)2},B={(x,y)∣(x−4)2+(y−5)2>(52)2}A=\{(x,y)|(x-3)^2+(y-4)^2\leq\left( \frac{5}{2}\right)^2\},B=\{(x,y)|(x-4)^2+(y-5)^2>\left( \frac{5}{2}\right)^2\}, then the number of integral points in A∩BA\cap B is________.
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