Question

Radius of a circle with centre 'O' is $4\sqrt{5}$. $AB$ is the diameter of the circel $AE\parallel BC,BC=8cm$. Line $EC$ is tangent to the circle at point $D$. Find the length of $DE$.

• A. $4\sqrt{5}$
• B. $6\sqrt{5}$
• C. $8$
• D. $10$

Answer 1

The correct option is D $10$

$AE\parallel BC$
$\therefore \angle OBC=90$
$AO=OD=OB=4\sqrt{5}cm$
$BC=8cm$
$OC=\sqrt{8^2+{4\sqrt{5}}^2}=12cm$
$\angle EOC={90}^o,$
$\therefore \frac{1}{{OD}^2}=\frac{1}{{OE}^2}+\frac{1}{{OC}^2}$
$\therefore OE=6\sqrt{5}cm$
$AE=10cm$ (By pythagorous)
$\therefore$ $ED=10cm$.

Hence, option D is correct.