MathDB

56

Part of 1986 IMO Longlists

Problems(1)

Construct M such that the sum is maximal

Source:

8/29/2010
Let A1A2A3A4A5A6A_1A_2A_3A_4A_5A_6 be a hexagon inscribed into a circle with center OO. Consider the circular arc with endpoints A1,A6A_1,A_6 not containing A2A_2. For any point MM of that arc denote by hih_i the distance from MM to the line AiAi+1 (1≤i≤5)A_iA_{i+1} \ (1 \leq i \leq 5). Construct MM such that the sum h1+⋯+h5h_1 + \cdots + h_5 is maximal.
geometry proposedgeometry