There are 6 equally spaced points A, B, C, D, E and F marked on a circle with radius R. How many con

Question

There are 6 equally spaced points A, B, C, D, E and F marked on a circle with radius R. How many convex heptagons of distinctly different areas can be drawn using these points as vertices?

Accepted Answer

{"type":"doc","content":[{"content":[{"marks":[{"type":"bold"}],"text":"Step 1 (Analyze Polygon Definition):","type":"text"},{"text":" A heptagon is defined as a polygon with exactly 7 vertices (and 7 sides).","type":"text"}],"type":"paragraph"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 2 (Analyze available vertices):","type":"text"},{"text":" The problem states that there are 6 equally spaced points marked on a circle. To draw any polygon using these points as vertices, we must choose our vertices strictly from this set of 6 points.","type":"text"},{"type":"hard_break"},{"type":"text","text":"Since the maximum number of available points is 6, it is mathematically impossible to choose 7 distinct vertices to draw a heptagon."}],"type":"paragraph"},{"type":"paragraph","content":[{"marks":[{"type":"bold"}],"text":"Step 3 (Conclusion):","type":"text"},{"text":" The number of convex heptagons that can be drawn is exactly ","type":"text"},{"marks":[{"type":"code"}],"text":"0","type":"text"},{"text":".","type":"text"}]}]}

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