Question

In the figure given, $AB$ is a diameter of a circle and $CD$ is perpendicular to $AB$; if $AB=10cm$ and $AE=2cm$, then what is the length of $ED$?

• A. $50$
• B. $16$
• C. $\sqrt{10}$
• D. $\sqrt{20}$

Answer 1

Answer: (B)

$16$

R.E.F image

$AB=10$

$AE=2$

$ED=(?)$

Assuming O as an center of

the circle

Now taking an bisector

from D such as $OD=OB=r$

$\therefore OD=10/2=5cm$

$OE=OA-AE$

$=5-2$

$=3cm$

in $\Delta OED$

$O{E}^2+E{D}^2=O{D}^2\to \left(i\right)$

Substituting the value in (i)

$(3{)}^2+E{D}^2=(5{)}^2$

$\therefore E{D}^2=25-9$

$E{D}^2=16$

$\therefore ED=16$