Question Number 16940 by Tinkutara last updated on 28/Jun/17
$$\mathrm{Six}\:\mathrm{points}\:\mathrm{A},\:\mathrm{B},\:\mathrm{C},\:\mathrm{D},\:\mathrm{E},\:\mathrm{and}\:\mathrm{F}\:\mathrm{are} \\ $$$$\mathrm{placed}\:\mathrm{on}\:\mathrm{a}\:\mathrm{square}\:\mathrm{rigid},\:\mathrm{as}\:\mathrm{shown}. \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{triangles}\:\mathrm{that}\:\mathrm{are}\:\boldsymbol{\mathrm{not}} \\ $$$$\mathrm{right}-\mathrm{angled}\:\mathrm{can}\:\mathrm{be}\:\mathrm{drawn}\:\mathrm{by}\:\mathrm{using}\:\mathrm{3} \\ $$$$\mathrm{of}\:\mathrm{these}\:\mathrm{6}\:\mathrm{points}\:\mathrm{as}\:\mathrm{vertices}? \\ $$
Commented by Tinkutara last updated on 28/Jun/17
Answered by ajfour last updated on 28/Jun/17
$$\:\mathrm{i}\:\mathrm{could}\:\mathrm{see}\:\mathrm{only}\:\mathrm{4}\:\mathrm{such}\:\mathrm{triangles}. \\ $$
Commented by Tinkutara last updated on 28/Jun/17
$$\mathrm{Can}\:\mathrm{you}\:\mathrm{explain}? \\ $$
Commented by ajfour last updated on 28/Jun/17
$$\bigtriangleup\mathrm{DEC},\:\bigtriangleup\mathrm{AEF},\:\bigtriangleup\mathrm{ABF},\:\bigtriangleup\mathrm{BCD}\:. \\ $$