Menu Close

Question-187721




Question Number 187721 by Mingma last updated on 20/Feb/23
Answered by mr W last updated on 21/Feb/23
Commented by mr W last updated on 21/Feb/23
due to similarity of triangles:  (a/d)=(u/y)  similarly  (e/b)=(w/u)  (c/f)=(y/w)  ⇒(a/d)×(e/b)×(c/f)=(u/y)×(w/u)×(y/w)=1  ⇒((ace)/(bdf))=1  ⇒ace=bdf ✓
$${due}\:{to}\:{similarity}\:{of}\:{triangles}: \\ $$$$\frac{{a}}{{d}}=\frac{{u}}{{y}} \\ $$$${similarly} \\ $$$$\frac{{e}}{{b}}=\frac{{w}}{{u}} \\ $$$$\frac{{c}}{{f}}=\frac{{y}}{{w}} \\ $$$$\Rightarrow\frac{{a}}{{d}}×\frac{{e}}{{b}}×\frac{{c}}{{f}}=\frac{{u}}{{y}}×\frac{{w}}{{u}}×\frac{{y}}{{w}}=\mathrm{1} \\ $$$$\Rightarrow\frac{{ace}}{{bdf}}=\mathrm{1} \\ $$$$\Rightarrow{ace}={bdf}\:\checkmark \\ $$
Commented by Rupesh123 last updated on 21/Feb/23
Nice work, bro!

Leave a Reply

Your email address will not be published. Required fields are marked *