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The Number of Isosceles Triangles

Source: 1983 National High School Mathematics League, Exam One, Problem 7

February 21, 2020

Problem Statement

PP is a point on the plane which square ABCDABCD belongs to, satisfying that △PAB,△PBC,△PCD,△PDA\triangle PAB,\triangle PBC,\triangle PCD,\triangle PDA are isosceles triangles. What's the number of such points? (A)9(B)17(C)1(D)5\text{(A)}9\qquad\text{(B)}17\qquad\text{(C)}1\qquad\text{(D)}5
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