Question-151444

Question Number 151444 by liberty last updated on 21/Aug/21

Answered by mr W last updated on 21/Aug/21

say BE=diameter=2×AB ((BC)/(BO))=((BO)/(BE)) ⇒BC×BE=BO^2 ⇒BC×2×AB=BO^2 ⇒[ABCD]=BC×AB=((BO^2 )/2)=((10^2 )/2)=50

$${say}\:{BE}={diameter}=\mathrm{2}×{AB} \\ $$$$\frac{{BC}}{{BO}}=\frac{{BO}}{{BE}} \\ $$$$\Rightarrow{BC}×{BE}={BO}^{\mathrm{2}} \\ $$$$\Rightarrow{BC}×\mathrm{2}×{AB}={BO}^{\mathrm{2}} \\ $$$$\Rightarrow\left[{ABCD}\right]={BC}×{AB}=\frac{{BO}^{\mathrm{2}} }{\mathrm{2}}=\frac{\mathrm{10}^{\mathrm{2}} }{\mathrm{2}}=\mathrm{50} \\ $$

Commented by mr W last updated on 21/Aug/21