Question Number 28240 by $@ty@m last updated on 22/Jan/18
Answered by ajfour last updated on 22/Jan/18
$${DE}×{EA}={CE}×{EF} \\ $$$$\mathrm{6}×\mathrm{2}=\mathrm{6}\sqrt{\mathrm{2}}×{EF} \\ $$$$\Rightarrow\:\:{EF}=\sqrt{\mathrm{2}}\:\:{so}\:\:{CF}=\mathrm{7}\sqrt{\mathrm{2}} \\ $$$${let}\:{foot}\:{of}\:\bot\:{from}\:{F}\:{on}\:{BC}\:{be}\:{G}. \\ $$$${CG}=\mathrm{7}\:,\:{GB}=\mathrm{1},\:{FG}=\mathrm{7} \\ $$$${BF}^{\:\:\mathrm{2}} \:={GB}^{\:\mathrm{2}} +{FG}^{\:\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:=\mathrm{1}+\mathrm{49}\:=\mathrm{50} \\ $$$${BF}\:=\mathrm{5}\sqrt{\mathrm{2}}\:\:\approx\:\mathrm{7}.\mathrm{07} \\ $$
Commented by $@ty@m last updated on 22/Jan/18
$${Thank}\:{you}\:{very}\:{much}. \\ $$