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A 21-gon

Source: Indian RMO 1995 Problem 6

October 26, 2005
geometrycircumcircleindia

Problem Statement

Let A1A2A3…A21A_1A_2A_3 \ldots A_{21} be a 21-sided regular polygon inscribed in a circle with centre OO. How many triangles AiAjAkA_iA_jA_k, 1≤i<j<k≤211 \leq i < j < k \leq 21, contain the centre point OO in their interior?
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