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Three regular polygons have one vertex in common and just fill the whole space at that vertex. If the number of sides of the polygons are a, b, c respectively, prove that 1/a + 1/b + 1/c = 1/2 . Also find all possible (a, b, c) with a ≤ b ≤ c.

Three regular polygons have one vertex in common and just fill the whole space at that vertex. If the number of sides of the polygons are a, b, c respectively, prove that 1/a + 1/b + 1/c = 1/2 . Also find all possible (a, b, c) with a ≤ b ≤ c.

Grade:9

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