MathDB

3

Part of 2008 Danube Mathematical Competition

Problems(1)

length of sum of 2n vectors from center of a semicircle is an odd integer

Source: Danube 2008 p3

7/22/2019
On a semicircle centred at OO and with radius 11 choose the respective points A1,A2,...,A2nA_1,A_2,...,A_{2n} , for n∈N∗n \in N^*. The lenght of the projection of the vector u→=OA1→+OA2→+...+OA2n→\overrightarrow {u}=\overrightarrow{OA_1} +\overrightarrow{OA_2}+...+\overrightarrow{OA_{2n}} on the diameter is an odd integer. Show that the projection of that vector on the diameter is at least 11.
geometryvectorSumsemicircleprojectiongeometric inequality