Let P be a convex polygon with 50 vertices. A set F of diagonals of P is said to be minimally friend

Question

Let P be a convex polygon with 50 vertices. A set F of diagonals of P is said to be minimally friendly if any diagonal d in F intersects at most one other diagonal in F at a point interior to P. Find the largest possible number of elements in a minimally friendly set. F.

Accepted Answer

{"content":[{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 1:"},{"text":" Total number of non-intersecting diagonals","type":"text"}],"type":"paragraph"},{"content":[{"text":"Step 2:","type":"text","marks":[{"type":"bold"}]},{"text":" A1A3, A1A4, A1A5,.., A1A4, → 47","type":"text"}],"type":"paragraph"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 3:","type":"text"},{"text":" Total number of intersecting diagonals at only one point to the non-intersecting diagonals","type":"text"}],"type":"paragraph"},{"type":"paragraph","content":[{"marks":[{"type":"bold"}],"text":"Step 4:","type":"text"},{"text":" A2A4, A4A6, A6A8, …., A48A50 → 24","type":"text"}]},{"content":[{"text":"Step 5:","type":"text","marks":[{"type":"bold"}]},{"text":" Total = 47 + 24 = 71","type":"text"}],"type":"paragraph"}],"type":"doc"}

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