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Question Number 185869 by Mingma last updated on 29/Jan/23

Answered by mr W last updated on 29/Jan/23

Commented by mr W last updated on 29/Jan/23

75°+60°+45°=180°  ⇒D,E,F are collinear!

$$\mathrm{75}°+\mathrm{60}°+\mathrm{45}°=\mathrm{180}° \\ $$$$\Rightarrow{D},{E},{F}\:{are}\:{collinear}! \\ $$

Answered by ajfour last updated on 29/Jan/23

E((a/2), ((a(√3))/2))    F(a+((a(√3))/2) , (a/2))  D(0,a)  slope of EF=−((((√3)−1)/( (√3)+1)))  slope of DE=−(2−(√3))  and they are equal!

$${E}\left(\frac{{a}}{\mathrm{2}},\:\frac{{a}\sqrt{\mathrm{3}}}{\mathrm{2}}\right)\:\:\:\:{F}\left({a}+\frac{{a}\sqrt{\mathrm{3}}}{\mathrm{2}}\:,\:\frac{{a}}{\mathrm{2}}\right)\:\:{D}\left(\mathrm{0},{a}\right) \\ $$$${slope}\:{of}\:{EF}=−\left(\frac{\sqrt{\mathrm{3}}−\mathrm{1}}{\:\sqrt{\mathrm{3}}+\mathrm{1}}\right) \\ $$$${slope}\:{of}\:{DE}=−\left(\mathrm{2}−\sqrt{\mathrm{3}}\right) \\ $$$${and}\:{they}\:{are}\:{equal}! \\ $$

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