Question Number 42112 by Raj Singh last updated on 18/Aug/18
Commented by Raj Singh last updated on 18/Aug/18
$${if}\:{OF}\:{and}\:{OE}\:{is}\:{bisector}\:{of}\:<{BOC} \\ $$$${and}\:<{AOC}\:{and}\:{OE}\:{perpendicalr} \\ $$$${to}\:{OF}\:\:{then}\:{prove}\:{that}\:{A}\:{O}\:{B}\:{is}\:{linear} \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 18/Aug/18
$${oF}\:{bisector}\:{of}\angle{BOC} \\ $$$$\angle{BOF}=\angle{FOC}={x} \\ $$$$\angle{BOC}=\mathrm{2}{x} \\ $$$$\angle{AOE}=\angle{EOC}={y} \\ $$$$\angle{AOC}=\mathrm{2}{y} \\ $$$${Given}\:{EO}\bot{OF}\:\:\:{so} \\ $$$$\angle{EOC}+\angle{COF}={y}+{x}=\mathrm{90}^{{o}} \\ $$$${now}\:\angle{AOC}+\angle{BOC}=\mathrm{2}{x}+\mathrm{2}{y}=\mathrm{2}\left({x}+{y}\right)=\mathrm{180}^{{o}} \\ $$$${hence}\:{A},{O}\:{andB}\:{lies}\:{on}\:{a}\:{line} \\ $$