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Six-points-A-B-C-D-E-and-F-are-placed-on-a-square-rigid-as-shown-How-many-triangles-that-are-not-right-angled-can-be-drawn-by-using-3-of-these-6-points-as-vertices-




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

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