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CEMC Gauss (Grade 8), 2006

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer Canada

In the diagram, the points are evenly spaced vertically and horizontally. A segment $AB$ is drawn using two of the points, as shown. Point $C$ is chosen to be one of the remaining $18$ points. For how many of these $18$ possible points is triangle $ABC$ isosceles?

(A) $6$ (B) $4$ (C) $5$ (D) $2$ (E) $3$

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