5

Part of 2010 IMAC Arhimede

Problems(1)

n points create always obtuse triangles, prove n+1 do it also

Source: IMAC Arhimede 2010 p5

Different points

A_1, A_2,..., A_n

n> 3

) are such that the triangle

A_iA_jA_k

is obtuse for all the different

i,j,k \in\{1,2,...,n\}

. Prove that there is a point

A_{n + 1}

in the plane, such that the triangle

A_iA_jA_{n + 1}

is obtuse for all different

i,j \in\{1,2,...,n\}

combinatoricscombinatorial geometrypointsObtuse triangle