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sum of n - 1 angles is 30^o, n equal parts of side of equilateral

Source: TOT 493 1996 Spring J A6 Tournament Of Towns

August 16, 2024
geometryangles

Problem Statement

In an equilateral triangle ABCABC, let DD be a point on the side ABAB such that AD=AB/nAD = AB /n. Prove that the sum of n−1n - 1 angles ∠DPlA\angle DP_lA, ∠DP2A\angle DP_2A, ......, ∠DPnA\angle DP_nA where P1P_1, P2P_2, ...... ,Pn−1P_{n-1} are the points dividing the side BCBC into nn equal parts, is equal to 3030 degrees if
(a) n=3n = 3 (b) nn is an arbitrary integer, n>2n > 2.
(V Proizvolov)
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